Quadrant Model of Reality Book 11 Art

Art chapter

The Jvari church is an early example of a "four-apsed church with four niches"[2] domed tetraconch. Between the four apses are three-quarter cylindrical niches which are open to the central space, and the transition from the square central bay to the base of the dome's drum is effected through three rows of squinches. This "four-apses four-niches" church design is found in the architecture of Georgia, Armenia, and Caucasian Albania, and is often referred to as a "Hripsime-type plan" after its best known example, the church of St. Hripsime in Armenia. The Jvari church had a great impact on the further development of Georgian architecture and served as a model for many other churches.

Varied bas-relief sculptures with Hellenistic and Sasanian influences decorate its external façades, some of which are accompanied by explanatory inscriptions in Georgian Asomtavruli script. The entrance tympanum on the southern façade is adorned with a relief of the Glorification of the Cross, the same façade also shows an Ascension of Christ.

Uncertainty over, and debate about, the date of the church's construction have assumed nationalist undertones in Georgia and Armenia, with the prize being which nation can claim to have invented the "four-apsed church with four niches" form.

QMRNinotsminda Cathedral (Georgian: ნინოწმინდის მონასტერი) (c. 575) is located in the village of Sagarejo, in the Kakheti region, Georgia.

Ninotsminda Cathedral is highly significant to the development of Georgian architecture, as it predates Jvari Monastery in Mtskheta, and served as a model for the development of the later tetraconch (four-apse) form.[citation needed] The site is ruins today, with only the eastern apse and a portion of the western wall remaining. The ruined apse is decorated with 16th century frescos of the Hodegetria, severely vandalised with bullet holes from Dagestani bandits in the 18th and 19th centuries. Outlines of the foundations indicate that the church originally had an octagonal center, surrounded by corner niches. Historical records indicate that restoration work was undertaken in the 10th and 11th centuries, and also during 1671 and 1774. However, the cathedral collapsed during earthquakes in 1824 and 1848 and was not reconstructed.

The large brick belltower within the same complex dates from the reign of King Levan of Kakheti (1520-1574). The lower three stories served as a residence, each floor with a fireplace. The staggered placement of bricks on the exterior façade to form geometric patterns indicates the cultural influence of Safavid Persia, as does the pointed arch over the entrance.

The Ninotsminda complex is surrounded by a fortification, with corner towers and a crenalated curtain wall, dating from the 16th-17th centuries. The fortified entrance gate has protruding towers with beehive machicolations.

The complex is currently operated as a nunnery by the Georgian Orthodox Church, and reconstruction work is underway.

QMRSaint Hripsime Church (Armenian: Սուրբ Հռիփսիմե եկեղեցի, Surb Hřip’simē yekeghetsi) is a seventh Armenian Apostolic century church in the city of Vagharshapat (Etchmiadzin), Armenia. It is one of the oldest surviving churches in the country. The church was erected by Catholicos Komitas atop the original mausoleum built by Catholicos Sahak the Great in 395 AD that contained the remains of the martyred Saint Rhipsime (Hripsime) to whom the church was dedicated. The structure was completed in 618 AD. It is known for its fine Armenian-style architecture of the classical period, which has influenced many other Armenian churches since. It was listed as a UNESCO World Heritage Site along with other nearby churches.

It is a four apse church

Flag of the Solomon Islands

From Wikipedia, the free encyclopedia

Solomon Islands

Flag of the Solomon Islands.svg

Flag of Solomon Islands

Use National flag

Proportion 1:2

Adopted 18 November 1977

Design A blue and green flag divided by a yellow diagonal radiating from the lower-hoist side corner; with five white, five-pointed stars (2-1-2) in the canton.

The national flag of Solomon Islands was adopted officially on 18 November 1977.

Contents [hide]

1 Make up

2 Variants

3 Historical flags

4 References

5 External links

Make up[edit]

The five main island groups are represented by the five stars.[1] The blue is supposed to represent the surrounding ocean, while the green represents the land. The yellow stripe is symbolic of the sunshine.

The civil ensign[2] (for merchant ships) and state ensign[3] (for non-military government vessels) are red and blue flags, respectively, with the national flag in the canton.

The naval ensign[4] (for police vessels) is based on the British white ensign, a red cross on a white field, also with the national flag in the canton.

QMRA saltire is a heraldic symbol in the form of a diagonal cross, like the shape of the letter X in Roman type. Saint Andrew is said to have been martyred on such a cross.

It appears in numerous flags, including those of Scotland and Jamaica, and other coats of arms and seals. A variant, also appearing on many past and present flags and symbols, is the Cross of Burgundy flag.

A warning sign in the shape of a saltire is also used to indicate the point at which a railway line intersects a road at a level crossing.

In Unicode, the cross is encoded at U+2613 ☓ saltire (HTML ☓). See X mark#Unicode for similar symbols that might be more accessible.

QMRIn the Western church four eminent "Fathers of the Church" attained this honour in the early Middle Ages: Saint Gregory the Great, Saint Ambrose, Saint Augustine, and Saint Jerome. The "four Doctors" became a commonplace among the Scholastics, and a decree of Boniface VIII (1298) ordering their feasts to be kept as doubles in the whole Church is contained in his sixth book of Decretals (cap. "Gloriosus", de relique. et vener. sanctorum, in Sexto, III, 22).[1]

In the Eastern Church three Doctors were pre-eminent: Saint John Chrysostom, Saint Basil the Great, and Saint Gregory Nazianzen. The feasts of these three saints were made obligatory throughout the Eastern Empire by Leo VI the Wise. A common feast was later instituted in their honour on 30 January, called "the feast of the three Hierarchs". In the Menaea for that day it is related that the three Doctors appeared in a dream to John Mauropous, Bishop of Euchaitae, and commanded him to institute a festival in their honour, in order to put a stop to the rivalries of their votaries and panegyrists. This was under Alexius Comnenus (1081–1118; see "Acta SS.", 14 June, under St. Basil, c. xxxviii). But sermons for the feast are attributed in manuscripts to Cosmas Vestitor, who flourished in the tenth century. The three are as common in Eastern art as the four are in Western. Durandus (i, 3) remarks that Doctors should be represented with books in their hands. In the West analogy led to the veneration of four Eastern Doctors, Saint Athanasius being added to the three hierarchs.[1]

QMRThe saltire appears on vexilla that are represented consistently on coinage of Christian emperors of Rome, beginning in the fourth century. Anne Roes found it on coins of Constantius II, Valentinian, Jovian, Gratianus, Valens, Arcadius, Constantine III, Jovinus, Theodosius I, Eugenius and Theodosius II, though she searched only coins at the British Museum.[1] In the ninth and tenth century the saltire was revived in Constantinople as a symbol of Christian-imperial power.[citation needed]

Anne Roes detected the symbol, which often appears with balls in the quadrants formed by the arms of the chi-cross, in standards that appear on the coins of Persepolis. She suggested that early Christians endorsed its solar symbolism as appropriate to Christ. She also wrote: "although it cannot be proved, ... in the white saltire of St. Andrew we still have a reminiscence of the old standard of the Persepolitan kingdom".[2]

QMRThe Flag of Scotland, called The Saltire or St Andrew's Cross, is a blue field with a white saltire; according to tradition, it represents Saint Andrew, who is supposed to have been crucified on a cross of that form (called a crux decussata) at Patras. The St Andrew's Cross was worn as a badge on hats in Scotland, on the day of the feast of St. Andrew.[1]

The Cross of Burgundy, a form of the St. Andrew's Cross, is used in numerous flags across Europe and the Americas. It was first used in the 15th century as an emblem by the Valois Dukes of Burgundy. The Duchy of Burgundy, forming a large part of eastern France and the Low Countries, was inherited by the House of Habsburg on the extinction of the Valois ducal line. The emblem was therefore assumed by the monarchs of Spain as a consequence of the Habsburgs bringing together, in the early 16th century, their Burgundian inheritance with the other extensive possessions it inherited throughout Europe and the Americas, including the crowns of Castile and Aragon. As a result, the Cross of Burgundy has appeared in a wide variety of flags connected with territories formerly part of the Burgundian or Habsburg inheritance. Examples of such diversity include the Spanish naval ensign (1506-1701), the flag of Carlism (the nineteenth century Spanish conservative movement), the flag of the Dutch municipality of Eijsden and the flag of Chuquisaca in Bolivia.

Cross of Burgundy

The naval ensign of the Imperial Russian (1696–1917) and Russian navies (1991–present) is a blue saltire on a white field. Prior to the Union the Royal Scots Navy used a red ensign incorporating the St Andrew's Cross; this ensign is now sometimes flown as part of an unofficial civil ensign in Scottish waters. With its colours exchanged (and a lighter blue), the same design forms part of the arms and flag of Nova Scotia (whose name means "New Scotland"). The Brazilian cities of Rio de Janeiro and Fortaleza also use a blue saltire on a white field, with their coats-of-arms at the hub. The flags of the Spanish island of Tenerife and the remote Colombian islands of San Andrés and Providencia also use a white saltire on a blue field.

Saltires are also seen in several other flags, including the flags of Grenada, Jamaica, Alabama, Florida, Jersey, Logroño, Vitoria, Amsterdam, Breda, Katwijk, Potchefstroom and Valdivia, as well as the former Indian princely states of Khairpur, Rajkot and Jaora. The design is also part of the Confederate Battle Flag and Naval Jack used during the American Civil War (see Flags of the Confederate States of America). Arthur L. Rogers, designer of the final version of the Confederate National flag, claimed that it was based off the saltire of Scotland.[10]

Symbol[edit]

In the old European Union standard, a black saltire set in an orange square is the hazard symbol for irritants (Xi) or harmful chemicals (Xn). It indicates a hazard less severe than skull and crossbones, used for poisons, or the corrosive sign.

In the politics of Scotland, both the Scottish National Party and Scottish Conservative Party use stylised saltires as their party logos, deriving from the flag of Scotland.

The trademark of X-Radium stoneware, patented cooking ware produced in the early 1900s by F. H. Griswold, was an X with radiating lines.

Signage[edit]

Polish railway crossing sign, G-3 (single track)

A saltire is the conventional road sign used to indicate the point at which a railway line intersects a road at a level crossing, called a "crossbuck" in this context.

A white saltire on a blue background (or black on yellow for temporary signs) is displayed in UK railway signalling as a "cancelling indicator" for the Automatic Warning System (AWS), informing the driver that the received warning can be disregarded.

In Cameroon, a red "X" placed on illegally constructed buildings scheduled for demolition is occasionally referred to as a "St Andrew's Cross". It is usually accompanied by the letters "A.D." ("à détruire" - French for "to be demolished") and a date or deadline. During a campaign of urban renewal by the Yaoundé Urban Council in Cameroon, the cross was popularly referred to as "Tsimi's Cross" after the Government Delegate to Yaoundé Urban Council Gilbert Tsimi Evouna.[11]

Less formally, on occasions of political controversy in many countries and times the usage of marking the face of a political opponent on a poster with an "X" is a commonly understood way of expressing strong disapproval, sometimes even the wish to kill the person whose picture is so marked.

The Maria Theresa thaler has a saltire to symbolize the 1750 debasement of the coinage, from 9 to 10 thalers to a Vienna mark, a weight of silver. An "X" is the Roman numeral symbol for "10".

In traditional timber framing a pair of crossing braces is called both a saltire and St. Andrews Cross.[12] Half-timbering, particularly in France and Germany, has patterns of framing members forming many different symbols known as ornamental bracing.[13]

Gallery of saltires[edit]

Coat of arms of Barbados with Sugar Cane held in saltire.

Coat of arms of the Neville family

Tactical Recognition Flash of the Royal Regiment of Scotland

Saint Patrick's Flag

St Andrew's flag of the Russian and Imperial Russian Navy

Russian White Army flag of the General Markov Regiment

Saint Alban's Cross

Cross of Burgundy Flag (used by the Spanish Empire 1506–1701 as a naval ensign, and up to 1843 as the land battle flag)

Southern Cross

Flag of Alabama

Apopka, Florida

Flag of Amstelveen

Flag of Amsterdam

Flag of Ouder-Amstel

Flag of Arkhangelsk

Flag of the Basque Country, (the Ikurriña)

Flag of the Belgian Navy

Flag of Breda

Flag of Brevard County

Flag of El Bierzo

Flag of Castro Urdiales

Flag of Clay County

Flag of Collier County

Flag of Coral Springs

Flag of Florida

Flag of the Fortaleza (Ceará, Brazil)

Flag of Grenada

Flag of Hollywood, Florida

Flag of Jamaica

Flag of Jersey

Flag of Katwijk

Flag of Logroño

Flag of Luqa

Flag of Marsaxlokk

Flag of Miami-Dade County

Flag of Nova Scotia

Flag of Panama City, Florida

Flag of Potchefstroom, North West Province, South Africa

Flag of Rio de Janeiro

Flag of Senglea

Flag of Swieqi

Flag of Tallahassee

Flag of Tenerife

Flag of Żabbar

A blue-and-white saltire used on a road sign to represent the Flag of Scotland.

Flag of Newfoundland and Labrador

Russian Naval Jack

Flag of Novorossiya

Flag of San Andres and Providencia Department, Colombia.

Flag of Santo André, São Paulo

Flag of the former Indian princely state of Rajkot

Logo of the Christian Church (Disciples of Christ)

Royal Coat of arms of Spain (1700-1761)-Common Version of the Colours.svg

Royal Coat of arms of Spain (1761-1843) - Common Version of the Colours.svg

Royal Coat of arms of Spain

Common Version of the Standard Colours

(1700-1761)[14]

Royal Coat of arms of Spain

Common Version of the Standard Colours

(1761-1843)[14]

Lesser Coat of arms of Spain (1843-1868 and 1874-1931)-Version of the Colours.svg

Coat of arms of Spain (1871-1873)-Version of the Colours.svg

National Coat of arms of Spain (Until 1931)-Version of the Colours.svg

Coat of arms of Spain - Version of the Standard Colours

(1843-1868/1874-1931)

Variant with the lesser royal arms quarters[14]

Coat of arms of Spain - Version of the Standard Colours

(1871/1873)

Reign of King Amadeo[14]

Coat of arms of Spain - Version of the Standard Colours

(1874-1931)

Variant with the national quarters[14]

QMRIn numerical analysis, given a square grid in one or two dimensions, the five-point stencil of a point in the grid is made up of the point itself together with its four "neighbors". It is used to write finite difference approximations to derivatives at grid points. It is an example for numerical differentiation. In two dimensions it is a quadrant grid

QMRIn numerical mathematics, a non-compact stencil is a type of discretization method, where any node surrounding the node of interest may be used in the calculation. A non-compact stencil's computational time increases with an increase of layers of nodes used. Non-compact stencils may be compared to Compact stencils. It is a quadrant grid

QMRIn mathematics, especially in the areas of numerical analysis called numerical partial differential equations, a compact stencil is a type of stencil that uses only nine nodes for its discretization method in two dimensions. It uses only the center node and the adjacent nodes. For any structured grid utilizing a compact stencil in 1, 2, or 3 dimensions the maximum number of nodes is 3, 9, or 27 respectively. Compact stencils may be compared to non-compact stencils. Compact stencils are currently implemented in many partial differential equation solvers, including several in the topics of CFD, FEA, and other mathematical solvers relating to PDE's.[1][2]

Two Point Stencil Example[edit]

The two point stencil for the first derivative of a function is given by:

f'(x_{0})={\frac {f\left(x_{0}+h\right)-f\left(x_{0}-h\right)}{2h}}+O\left(h^{2}\right).

This is obtained from the Taylor series expansion of the first derivative of the function given by:

{\begin{array}{l}f'(x_{0})={\frac {f\left(x_{0}+h\right)-f(x_{0})}{h}}-{\frac {f^{(2)}(x_{0})}{2!}}h-{\frac {f^{(3)}(x_{0})}{3!}}h^{2}-{\frac {f^{(4)}(x_{0})}{4!}}h^{3}+\cdots \end{array}}.

Replacing h with -h, we have:

{\begin{array}{l}f'(x_{0})=-{\frac {f\left(x_{0}-h\right)-f(x_{0})}{h}}+{\frac {f^{(2)}(x_{0})}{2!}}h-{\frac {f^{(3)}(x_{0})}{3!}}h^{2}+{\frac {f^{(4)}(x_{0})}{4!}}h^{3}+\cdots \end{array}}.

Addition of the above two equations together results in the cancellation of the terms in odd powers of h:

{\begin{array}{l}2f'(x_{0})={\frac {f\left(x_{0}+h\right)-f(x_{0})}{h}}-{\frac {f\left(x_{0}-h\right)-f(x_{0})}{h}}-2{\frac {f^{(3)}(x_{0})}{3!}}h^{2}+\cdots \end{array}}.

{\begin{array}{l}f'(x_{0})={\frac {f\left(x_{0}+h\right)-f\left(x_{0}-h\right)}{2h}}-{\frac {f^{(3)}(x_{0})}{3!}}h^{2}+\cdots \end{array}}.

{\begin{array}{l}f'(x_{0})={\frac {f\left(x_{0}+h\right)-f\left(x_{0}-h\right)}{2h}}+O\left(h^{2}\right)\end{array}}.

Three Point Stencil Example[edit]

For example, the three point stencil for the second derivative of a function is given by:

{\begin{array}{l}f^{(2)}(x_{0})={\frac {f\left(x_{0}+h\right)+f\left(x_{0}-h\right)-2f(x_{0})}{h^{2}}}+O\left(h^{2}\right)\end{array}}.

This is obtained from the Taylor series expansion of the first derivative of the function given by:

{\begin{array}{l}f'(x_{0})={\frac {f\left(x_{0}+h\right)-f(x_{0})}{h}}-{\frac {f^{(2)}(x_{0})}{2!}}h-{\frac {f^{(3)}(x_{0})}{3!}}h^{2}-{\frac {f^{(4)}(x_{0})}{4!}}h^{3}+\cdots \end{array}}.

Replacing h with -h, we have:

{\begin{array}{l}f'(x_{0})=-{\frac {f\left(x_{0}-h\right)-f(x_{0})}{h}}+{\frac {f^{(2)}(x_{0})}{2!}}h-{\frac {f^{(3)}(x_{0})}{3!}}h^{2}+{\frac {f^{(4)}(x_{0})}{4!}}h^{3}+\cdots \end{array}}.

Subtraction of the above two equations results in the cancellation of the terms in even powers of h: {\begin{array}{l}0={\frac {f\left(x_{0}+h\right)-f(x_{0})}{h}}+{\frac {f\left(x_{0}-h\right)-f(x_{0})}{h}}-2{\frac {f^{(2)}(x_{0})}{2!}}h-2{\frac {f^{(4)}(x_{0})}{4!}}h^{3}+\cdots \end{array}}.

{\begin{array}{l}f^{(2)}(x_{0})={\frac {f\left(x_{0}+h\right)+f\left(x_{0}-h\right)-2f(x_{0})}{h^{2}}}-2{\frac {f^{(4)}(x_{0})}{4!}}h^{2}+\cdots \end{array}}.

{\begin{array}{l}f^{(2)}(x_{0})={\frac {f\left(x_{0}+h\right)+f\left(x_{0}-h\right)-2f(x_{0})}{h^{2}}}+O\left(h^{2}\right)\end{array}}.

QMRHigher derivatives[edit]

Let f be a differentiable function, and let f ′(x) be its derivative. The derivative of f ′(x) (if it has one) is written f ′′(x) and is called the second derivative of f. Similarly, the derivative of a second derivative, if it exists, is written f ′′′(x) and is called the third derivative of f. Continuing this process, one can define, if it exists, the nth derivative as the derivative of the (n-1)th derivative. These repeated derivatives are called higher-order derivatives. The nth derivative is also called the derivative of order n.

If x(t) represents the position of an object at time t, then the higher-order derivatives of x have physical interpretations. The second derivative of x is the derivative of x′(t), the velocity, and by definition this is the object's acceleration. The third derivative of x is defined to be the jerk, and the fourth derivative is defined to be the jounce.

A function f need not have a derivative, for example, if it is not continuous. Similarly, even if f does have a derivative, it may not have a second derivative. For example, let

f(x) = \begin{cases} +x^2, & \text{if }x\ge 0 \\ -x^2, & \text{if }x \le 0.\end{cases}

Calculation shows that f is a differentiable function whose derivative is

f'(x) = \begin{cases} +2x, & \text{if }x\ge 0 \\ -2x, & \text{if }x \le 0.\end{cases}

QMRA gopura is an entrance building. At Angkor, passage through the enclosure walls surrounding a temple compound is frequently accomplished by means of an impressive gopura, rather than just an aperture in the wall or a doorway. Enclosures surrounding a temple are often constructed with a gopura at each of the four cardinal points. In plan, gopuras are usually cross-shaped and elongated along the axis of the enclosure wall; if the wall is constructed with an accompanying gallery, the gallery is sometimes connected to the arms of the gopura. Many Angkorian gopuras have a tower at the centre of the cross. The lintels and pediments are often decorated, and guardian figures (dvarapalas) are often placed or carved on either side of the doorways.

QMRHall of Dancers[edit]

A Hall of Dancers is a structure of a type found in certain late 12th-century temples constructed under King Jayavarman VII: Ta Prohm, Preah Khan, Banteay Kdei and Banteay Chhmar. It is a rectangular building elongated along the temple's east axis and divided into four courtyards by galleries. Formerly it had a roof made of perishable materials; now only the stone walls remain. The pillars of the galleries are decorated with carved designs of dancing apsaras; hence scholars have suggested that the hall itself may have been used for dancing.

QMRLintel, pediment, and tympanum[edit]

A lintel is a horizontal beam connecting two vertical columns between which runs a door or passageway. Because the Angkorean Khmer lacked the ability to construct a true arch, they constructed their passageways using lintels or corbelling. A pediment is a roughly triangular structure above a lintel. A tympanum is the decorated surface of a pediment.

Lintel and pediment at Banteay Srei; the motif on the pediment is Shiva Nataraja.

The styles employed by Angkorean artists in the decoration of lintels evolved over time, as a result, the study of lintels has proven a useful guide to the dating of temples. Some scholars have endeavored to develop a periodization of lintel styles.[22] The most beautiful Angkorean lintels are thought to be those of the Preah Ko style from the late 9th century.[23]

Common motifs in the decoration of lintels include the kala, the nāga and the makara, as well as various forms of vegetation.[24] Also frequently depicted are the Hindu gods associated with the four cardinal directions, with the identity of the god depicted on a given lintel or pediment depending on the direction faced by that element. Indra, the god of the sky, is associated with East; Yama, the god of judgment and Hell, with South; Varuna, the god of the ocean, with West; and Kubera, god of wealth, with North.[25]

QMRQuincunx[edit]

A linga in the form of a quincunx, set inside a yoni, is carved into the riverbed at Kbal Spean.

A quincunx is a spatial arrangement of five elements, with four elements placed as the corners of a square and the fifth placed in the center. The five peaks of Mount Meru were taken to exhibit this arrangement, and Khmer temples was arranged accordingly in order to convey a symbolic identification with the sacred mountain. The five brick towers of the 10th-century temple known as East Mebon, for example, are arranged in the shape of a quincunx. The quincunx also appears elsewhere in designs of the Angkorian period, as in the riverbed

QMRA linga in the form of a quincunx, set inside a yoni, is carved into the riverbed at Kbal Spean.

QMRThe Peirce quincuncial projection[1] is a conformal map projection developed by Charles Sanders Peirce in 1879.

QMRThe Peirce quincuncial projection[1] is a conformal map projection developed by Charles Sanders Peirce in 1879.

The maturation of complex analysis led to general techniques for conformal mapping, where points of a flat surface are handled as numbers on the complex plane. While working at the U.S. Coast and Geodetic Survey, the American philosopher Charles Sanders Peirce published his projection in 1879 (Peirce 1879),[2] having been inspired by H. A. Schwarz's 1869 conformal transformation of a circle onto a polygon of n sides (known as the Schwarz–Christoffel mapping). In the normal aspect, Peirce's projection presents the Northern Hemisphere in a square; the Southern Hemisphere is split into four isosceles triangles symmetrically surrounding the first one, akin to star-like projections. In effect, the whole map is a square, inspiring Peirce to call his projection quincuncial, after the arrangement of five items in a quincunx.

After Peirce presented his projection, two other cartographers developed similar projections of the hemisphere (or the whole sphere, after a suitable rearrangement) on a square: Guyou in 1887 and Adams in 1925.[3] The three projections are transversal versions of each other (see related projections below).

QMRCosmatesque, or Cosmati, is a style of geometric decorative inlay stonework typical of the architecture of Medieval Italy, and especially of Rome and its surroundings, and derived from that of the Byzantine Empire. It was used most extensively for the decoration of church floors, but was also used to decorate church walls, pulpits, and bishop's thrones. The name derives from the Cosmati, the leading family workshop of marble craftsmen in Rome who created such geometrical decorations. The style spread across Europe, where it was used in the most prestigious churches; the high altar of Westminster Abbey, for example,[1][2] is decorated with a cosmatesque marble floor.

It takes the quincunx pattern of five points making a cross

QMRSaint John of the Cross, O.C.D. (Spanish: San Juan de la Cruz; 1542[1] – 14 December 1591), was a major figure of the Counter-Reformation, a Spanish mystic, a Roman Catholic saint, a Carmelite friar and a priest who was born at Fontiveros, Old Castile.

John of the Cross was a reformer of the Carmelite Order and is considered, along with Saint Teresa of Ávila, as a founder of the Discalced Carmelites. He is also known for his writings. Both his poetry and his studies on the growth of the soul are considered the summit of mystical Spanish literature and one of the peaks of all Spanish literature. He was canonized as a saint in 1726 by Pope Benedict XIII. He is one of the thirty-six Doctors of the Church.

QMRDrawing of the crucifixion by John of the Cross, which inspired Salvador Dalí

QMRAbū ʿAbdullāh Muhammad ibn Idrīs al-Shāfīʿī (Arabic: ابو عبدالله محمد بن إدريس الشافعيّ) is a Muslim jurist, who lived from (767 — 820 CE / 150 — 204 AH). Often referred to as 'Shaykh al-Islām', al-Shāfi‘ī was one of the four great Imams, whose legacy on juridical matters and teaching eventually led to the Shafi'i school of fiqh (or Madh'hab). He is often referred to as Imam al-Shafi‘i

QMRA four-centred arch, also known as a depressed arch or Tudor arch, is a low, wide type of arch with a pointed apex. It is much wider than its height and gives the visual effect of having been flattened under pressure. Its structure is achieved by drafting two arcs which rise steeply from each springing point on a small radius, and then turning into two arches with a wide radius and much lower springing point.

This type of arch, when employed as a window opening, lends itself to very wide spaces, decoratively filled with many narrow vertical mullions and horizontal transoms. The overall effect produces a grid-like appearance of regular, delicate, rectangular forms with an emphasis on the perpendicular. It is also employed as a wall decoration in which arcade and window openings form part of the whole decorative surface.

The style, known as Perpendicular Gothic, which evolved from this treatment, is specific to England, and is very similar to contemporary Spanish style in particular. It was employed to great effect through the 15th century and first half of the 16th, as Renaissance styles were much slower to arrive in England than in Italy and France.

It can be seen notably at the East End of Gloucester Cathedral where the East Window is said to be as large as a tennis court. There are three very famous royal chapels and one chapel-like Abbey which show the style at its most elaborate- Kings College Chapel, Cambridge; St George's Chapel, Windsor; Henry VII's Chapel at Westminster Abbey, and Bath Abbey. However, very many simpler buildings, especially churches, built during the wool boom in East Anglia, are fine examples of the style.

QMRIn English architecture, it is often known as a Tudor arch,[1] as it was a common architectural element during the reign of the Tudor dynasty (1485–1603). The Gothic period's pointed arch was blunted into the flattened Tudor arch. The Tudor arch, placed over the oriel window, or a bay window supported on a bracket or corbel, was a striking window design of the Tudor period.[2][3]

Use in Islamic architecture[edit]

The four-centred arch is widely used in Islamic architecture, especially that of Persianate cultures. For example, almost all iwans use this type of arch.

Ancient Roman civilization[edit]

The Etruscan people, whose territories in Italy encompassed what would eventually become Rome (Rix cited in Woodward 2008),[6] founded what is now the city of Marzabotto at the end of the 6th century BC. It was based onGreek Ionic ideas, and it was here that the main east-west and north-south axes of a town (the decumanus maximus and cardo maximus respectively) could first be seen in Italy.[2] According to Stanislawski,[2] there is little evidence that the Romans adopted the Etruscan model at Marzabatto early in their expansion. Instead, the Roman Grid was spread around the Mediterranean and into northern Europe later on, during the late Republic and early Empire.[2]

Straight road in the Province of Bergamo, Italy, following line of Roman Grid

The military expansion of this period facilitated the adoption of the grid form as standard: the Romans established castra (forts or camps) first as military centres; some of them developed into administrative hubs. The Roman grid was similar in form to the Greek version of a grid, but allowed for practical considerations. For example, Roman castra were often sited on flat land, especially close to or on important nodes like river crossings or intersections of trade routes.[4] The dimensions of the castra were often standard, with each of its four walls generally having a length of 2,150 feet (660 metres). Familiarity was the aim of such standardisation: soldiers could be stationed anywhere around the Empire, and orientation would be easy within established towns if they had a standard layout. Each would have the aforementioned decumanus maximus and cardo maximus at its heart, and their intersection would form the forum, around which would be sited important public buildings. Indeed, such was the degree of similarity between towns that Higgins states that soldiers "would be housed at the same address as they moved from castra to castra".[4] Pompeii has been cited by both Higgins[4] and Laurence[7] as the best preserved example of the Roman grid.

Outside of the castra, large tracts of land were also divided in accordance with the grid within the walls. These were typically 2,400 feet (730 metres) per side (called centuria), and contained 100 parcels of land (each called heredium).[8] The decumanus maximus and cardo maximus extended from the town gates out towards neighbouring settlements. These were lined up to be as straight as possible, only deviating from their path due to natural obstacles that prevented a direct route.[8]

While the imposition of only one town form regardless of region could be seen as an imposition of imperial authority, there is no doubting the practical reasoning behind the formation of the Roman grid. Under Roman guidance, the grid was designed for efficiency and interchangeability, both facilitated by and aiding the expansion of their empire.

The grid is a quadrant grid

Asia from the first millennium AD[edit]

As Japan and the Korean peninsula became politically centralized in the 7th century AD, those societies adopted Chinese grid-planning principles in numerous locations. In Korea, Gyeongju, the capital of Unified Silla, and Sanggyeong, the capital of Balhae, adapted the Tang Dynasty Chinese model. The ancient capitals of Japan, such as Fujiwara-Kyô (AD 694-710), Nara (Heijô-Kyô, AD 710-784), and Kyoto (Heian-Kyô, AD 794-1868) also adapted from Tang's capital, Chang'an. However, for reasons of defense, the planners of Tokyo eschewed the grid, opting instead for an irregular network of streets surrounding the Edo Castle grounds. In later periods, some parts of Tokyo were grid-planned, but grid plans are generally rare in Japan, and the Japanese addressing system is accordingly based on increasingly fine subdivisions, rather than a grid.

The grid-planning tradition in Asia continued through the beginning of the 20th century, with Sapporo, Japan (est. 1868) following a grid plan under American influence.

Europe and its colonies[edit]

Barcelona

Ouagadougou, 1930

New European towns were planned using grids beginning in the 12th century, most prodigiously in the bastides of southern France that were built during the 13th and 14th centuries. Medieval European new towns using grid plans were widespread, ranging from Wales to the Florentine region. Many were built on ancient grids originally established as Roman colonial outposts.

The Roman model was also used in Spanish settlements during the Reconquista of Ferdinand and Isabella. It was subsequently applied in the new cities established during the Spanish colonization of the Americas, after the founding of San Cristóbal de La Laguna (Canary Islands) in 1496. In 1573, King Phillip II of Spain compiled the Laws of the Indies to guide the construction and administration of colonial communities. The Laws specified a square or rectangular central plaza with eight principal streets running from the plaza's corners. Hundreds of grid-plan communities throughout the Americas were established according to this pattern, echoing the practices of earlier Indian civilizations.

The grid plan became popular with the start of the Renaissance in Northern Europe. In 1606, the newly founded city of Mannheim in Germany was the first Renaissance city laid out on the grid plan. Later came the New Town in Edinburgh and almost the entire city centre of Glasgow, and many planned communities and cities in Australia, Canada and the United States such as New Haven and Adelaide.

The baroque capital city of Malta, Valletta, dating back to the 16th Century, was built following a rigid grid plan of uniformly designed houses, dotted with palaces, churches and squares.

Early United States[edit]

Commissioners' Plan of 1811 for Manhattan.

Twenty American grids compared at a scale of 400 feet to the inch.

Many of the earliest cities in the United States, such as Boston, did not start with a grid system.[9] However, even in pre-revolutionary days some cities saw the benefits of such a layout. New Haven Colony, one of the earliest colonies in America, was designed with a tiny 9-square grid at its founding in 1638. On a grander scale, Philadelphia was designed on a rectilinear street grid in 1682: one of the first cities in North America to use a grid system.[10][11] At the urging of city founder William Penn, surveyor Thomas Holme designed a system of wide streets intersecting at right angles between the Schuylkill River to the west and the Delaware River to the east, including five squares of dedicated parkland. Penn advertised this orderly design as a safeguard against overcrowding, fire, and disease, which plagued European cities. Holme drafted an ideal version of the grid,[12] but alleyways sprouted within and between larger blocks as the city took shape. Arguably the most famous grid plan in history is the plan for New York City formulated in the Commissioners' Plan of 1811, a visionary proposal by the state legislature of New York for the development of most of Manhattan[13] above Houston Street.

The city blocks and streets of Barcelona as conceived by Ildefonso Cerdá. The blocks include wide open spaces that continue across the street to adjacent blocks.

A diagram of three city grids at the same scale showing the differences in dimensions and configuration

Washington, D.C., the capital of the United States, was planned under French-American architect Pierre Charles L'Enfant. Under the L'Enfant plan, the original District of Columbia was developed using a grid plan that is interrupted by diagonal avenues, most famously Pennsylvania Avenue. These diagonals are often connected by traffic circles, such as Dupont Circle and Washington Circle. As the city grew, the plan was duplicated to cover most of the remainder of the capital. Meanwhile, the core of the city faced disarray and the McMillan Plan, led by Senator James McMillan, was adopted to build a National Mall and a parks system that is still today a jewel of the city.

Often, some of the streets in a grid are numbered (First, Second, etc.), lettered, or arranged in alphabetical order. Downtown San Diego uses all three schemes: north-south streets are numbered from west to east, and east-west streets are split between a lettered series running southward from A through L and a series of streets named after trees or plants, running northward alphabetically from Ash to Walnut. As in many cities, some of these streets have been given new names violating the system (the former D Street is now Broadway, the former 12th Avenue is now Park Boulevard, etc.); this has meant that 2nd, not 1st, is the most common street name in the United States.[14]

An exception to the typical, uniform grid is the plan of Savannah, Georgia (1733), known as the Oglethorpe Plan. It is a composite, cellular city block consisting of four large corner blocks, four small blocks in between and a public square in the centre; the entire composition of approximately ten acres (four hectares) is known as a ward.[15] Its cellular structure includes all the primary land uses of a neighborhood and has for that reason been called fractal.[16] Its street configuration presages modern traffic calming techniques applied to uniform grids where certain selected streets become discontinuous or narrow, thus discouraging through traffic. The configuration also represents an example of functional shared space, where pedestrian and vehicular traffic can safely and comfortably coexist.[17]

In the westward development of the United States, the use of the grid plan was nearly universal in the construction of new settlements, such as in Salt Lake City (1870), Dodge City (1872) and Oklahoma City (1890). In these western cities the streets were numbered even more carefully than in the east to suggest future prosperity and metropolitan status.[10]

One of the main advantages of the grid plan was that it allowed the rapid subdivision and auction of a large parcel of land. For example, when the legislature of the Republic of Texas decided in 1839 to move the capital to a new site along the Colorado River, the functioning of the government required the rapid population of the town, which was named Austin. Charged with the task, Edwin Waller designed a fourteen-block grid that fronted the river on 640 acres (exactly 1 square mile; about 2.6 km²). After surveying the land, Waller organized the almost immediate sale of 306 lots, and by the end of the year the entire Texas government had arrived by oxcart at the new site. Apart from the speed of surveying advantage, the rationale at the time of the grid's adoption in this and other cities remains obscure.

Late 19th century to the present[edit]

Ildefonso Cerdá, a Spanish civil engineer, defined a concept of urban planning, based on the grid, that he applied to the Eixample of Barcelona. The Eixample grid introduced innovative design elements which were exceptional at the time and even unique among subsequent grid plans:

a very large block measuring 113 by 113 m (371 by 371 ft), far larger than the old city blocks and larger than any Roman, Greek blocks and their mutations (see drawing below);

a 20 m (66 ft) road width (right of way) compared to mostly 3 m in the old city;

square blocks with truncated corners; and

major roads, perpendicular and diagonal, measuring 50 m (160 ft) in width.

These innovations he based on functional grounds: the block size, to enable the creation of a quiet interior open space (60 m by 60 m) and allow ample sunlight and ventilation to its perimeter buildings; the rectilinear geometry, the wide streets and boulevards to sustain high mobility and the truncated corners to facilitate turning of carts and coaches and particularly vehicles on fixed rails.[18]

In maps of larger American cities the downtown areas are almost always grids. These areas represent the original land dimensions of the founded city, generally around one square mile. Some cities expanded the grid further out from the centre, but maps also show that, in general, as the distance from the centre increases, a variety of patterns emerge in no particular discernible order. In juxtaposition to the grid they appear random. These new patterns have been systematically classified and their design characteristics measured[19]

In the United States, the grid system was widely used in most major cities and their suburbs until the 1960s. However, during the 1920s, the rapid adoption of the automobile caused a panic among urban planners, who, based on observation, claimed that speeding cars would eventually kill tens of thousands of small children per year. Apparently, at this early stage of the car's entry into the grid, the streets of major cities worldwide were the scene of virtual "slaughter" as the fatality rate in proportion to population was more than double the current rate.[20][21] In 2009, after several decades of road safety improvements and a continuous decline in fatalities, an estimated 33,963 people died in motor vehicle traffic crashes and, according to the National Highway Traffic Safety Administration, "Motor vehicle crashes are the leading cause of death for children from 3 to 14 years old.".[22] Planners, therefore, called for an inwardly focused "superblock" arrangement that minimized through automobile traffic and discouraged cars from traveling on anything but arterial roads; traffic generators, such as apartment complexes and shops, would be restricted to the edges of the superblock, along the arterial. This paradigm prevailed between about 1930 and 1960, especially in Los Angeles, where notable examples include Leimert Park (an early example) and Panorama City (a late-period one).

A prominent 20th century urbanist, Lewis Mumford, severely criticized some of the grid's characteristics: "With a T-square and a triangle, finally, the municipal engineer could, without the slightest training as either an architect or a sociologist, 'plan' a metropolis, with its standard lots, its standard blocks, its standard street widths, in short, with its standardized comparable, and replaceable parts. The new gridiron plans were spectacular in their inefficiency and waste. By usually failing to discriminate sufficiently between main arteries and residential streets, the first were not made wide enough while the second were usually too wide for purely neighborhood functions... as for its contribution to the permanent social functions of the city, the anonymous gridiron plan proved empty."[23]

In the 1960s, traffic engineers and urban planners abandoned the grid virtually wholesale in favor of a "street hierarchy". This is a thoroughly "asymmetric" street arrangement in which a residential subdivision—often surrounded by a noise wall or a security gate—is completely separated from the road network except for one or two connections to arterial roads. In a way, this is a return to medieval styles: as noted in Spiro Kostof's seminal history of urban design, The City Shaped, there is a strong resemblance between the street arrangements of modern American suburbs and those of medieval Arab and Moorish cities. In each case, the community unit at hand—the clan or extended family in the Muslim world, the economically homogeneous subdivision in modern suburbia—isolates itself from the larger urban scene by using dead ends and culs-de-sac.

Milton Keynes[edit]

Main article: Milton Keynes grid road system

One famous grid system is in the British new town of Milton Keynes. In this planned city, which began construction in 1967, a system of ten "horizontal" (roughly east-west) and eleven "vertical" (roughly north-south) roads was used, with roundabouts at each intersection. The horizontal roads were all given names ending in 'way' and H numbers (for 'horizontal', e.g. H3 Monks Way). The vertical roads were given names ending in 'street' and V numbers (for 'vertical', e.g. V6 Grafton Street). Each grid road was spaced roughly one kilometre along from the next, forming squares of approximately one square kilometre. Each square and each roundabout was given its own name. The system provided very easy transport within the city, although it confused visitors who were unfamiliar with the system. The grid squares thus formed are far larger than the city blocks described earlier, and the road layouts within the grid squares are generally 'organic' in form – matching the street hierarchy model described above.

Financial cost[edit]

The infrastructure cost for regular grid patterns is generally higher than for patterns with discontinuous streets. Costs for streets depend largely on four variables: street width, street length, block width and pavement width.

Block sizes and street length

In a numbered grid system, adding an extra street can cause confusion

Street width, or right of way (ROW), influences the amount of land that is devoted to streets, which becomes unavailable for development and therefore represents an opportunity cost. The wider the street the higher the opportunity cost. Street width is determined by circulation and aesthetic considerations and is not dependent on the pattern configuration. Any configuration can have wide or narrow streets.

Street length influences proportionately the amount of street components that have to be constructed such as pavement, curbs and sidewalks, storm sewers and drains, light poles, and trees. The street length of a given area of development depends on the frequency at which streets occur which in turn depends on the length and width of a block. The higher the frequency of streets the longer is their total length. The smaller the block dimensions the higher the frequency of the streets. As the frequency of street increases so does the number of intersections. Intersections normally cost more than straight street length because they are labour-intensive and require street and traffic signage.

Pavement width influences the cost by affecting the amount of materials and labour required to provide a finished road surface. Pavement width is generally based on traffic engineering considerations and is not dependent on pattern configuration. As with the street width, any pattern can have wide or narrow pavements. Of all three factors that affect cost, street width, street length and pavement width, only street length is pattern dependent. An objective cost comparison would, therefore, rely on this variable with the full understanding that the other variables, though optional, can play a role.

Traditional orthogonal grid patterns generally have greater street frequencies than discontinuous patterns. For example, Portland's block is 200 feet × 200 feet while Miletus' is half that size and Timgad's half again (see diagram). Houston, Sacramento and Barcelona are progressively bigger reaching up to four times the area of Portland's block. New York's 1811 plan (see above) has blocks of 200 ft. in width and variable lengths ranging from about 500 to 900 feet. The corresponding frequency of streets for each of these block sizes affects the street length.

A simple example of a grid street pattern (see diagram) illustrates the progressive reduction in total street length (the sum of all individual street lengths) and the corresponding increase in block length. For a corresponding reduction of one, two, three and four streets within this 40-acre (16 ha) parcel, the street length is reduced from an original total of 12,600 to 7,680 linear feet, a 39% reduction. Simultaneously, block lengths increase from 200 × 200 feet to 1240 × 200 feet. When all five blocks have reached the ultimate size of 1240 feet, four street lengths out of total eight have been eliminated. Block lengths of 1000 feet or larger rarely appear in grid plans and are not recommended as they hinder pedestrian movement (Pedestrianism, below). From the pedestrian perspective, the smaller the block is, the easier the navigation and the more direct the route. Consequently, the finer grids are preferred.

Patterns that incorporate discontinuous street types such as crescents and culs-de-sac have not, in general, regarded pedestrian movement as a priority and, consequently, have produced blocks that are usually in the 1000-foot range and often exceed it. As a result, street frequency drops and so does the total street length and, therefore, the cost. In general, it is not the street pattern per se that affects costs but the frequency of streets that it either necessitates or purposely incorporates.

An inherent advantage of the orthogonal geometry of a proper grid is its tendency to yield regular lots in well-packed sequences. This maximizes the use of the land of the block; it does not, however, affect street frequency. Any frequency of orthogonal streets produces the same packing[disambiguation needed] effect. Orthogonal geometry also minimizes disputes over lot boundaries and maximizes the number of lots that could front a given street. John Randal said Manhattan's grid plan facilitated "buying, selling and improving real estate".[10]

Another important aspect of street grids and the use of rectilinear blocks is that traffic flows of either pedestrians, cars, or both, only cross at right angles. This is an important traffic safety feature, since no one entering the intersection needs to look over their shoulder to see oncoming traffic. Any time traffic flows meet at an acute angle, someone cannot see traffic approaching them. The grid is thus a geometric response to our human physiology. It is very likely the original purpose of grid layouts comes from the Athenian Agora. Before the grid organization, markets were laid out randomly in a field with traffic approaches at odd angles. This caused carts and wagons to turn over due to frequent collisions. Laying out the market stalls into regularized rows at right angles solved this problem and was later built into the Athenian Agora and copied ever since.

Ecological features, rain water absorption and pollutant generation[edit]

Typical uniform grids are unresponsive to topography. Priene's plan, for example, is set on a hill side and most of its north-south streets are stepped, a feature that would have made them inaccessible to carts, chariots and loaded animals. Many modern cities follow Priene's example, e.g. San Francisco, Vancouver, and Saint John, New Brunswick. In a modern context, steep grades limit accessibility by car, and more so by bicycle, on foot, or wheelchair, particularly in cold climates.

The same inflexibility of the grid leads to disregarding environmentally sensitive areas such as small streams and creeks or mature woodlots in preference for the application of the immutable geometry. It is said of the NY grid plan that it flattened all obstacles in its way. By contrast, recent discontinuous street patterns follow the configuration of natural features without disrupting them. The grid represents a rationalist, reductionist solution to a multifaceted issue.

The grid's inherent high street and intersection frequencies produce large areas of impermeable surfaces in the street pavement and the sidewalks. In comparison to recent networks with discontinuous street types, grids can be up to 30% higher in impermeable surfaces attributable to roads. The emerging environmental priority of retaining as much as 90% of rain water on site becomes problematic with high percentages of impermeable surfaces. And since roads constitute the largest share of the total impermeable surfaces of a development, the difficulty is compounded by the grid type of layout. For these reasons modern planners have attempted to modify the rigid, uniform, classic grid.

Some cities, notably Seattle, have devised means to improve a street's retention capacity. However, frequent intersections as they occur in a regular grid would pose an obstacle to their effective application.

A street network pattern can affect the production of pollutants by the amount of car travel that it necessitates and the speed at which cars can travel. The grid plan with its frequent intersections may displace a portion of the local car trips with walking or biking due to the directness of route that it offers to pedestrians. But it also makes the same routes more direct for cars, which could be an enticement for driving. The potential car trip displacement would result in a reduction of pollutant emissions. The advantage of the intersection density for pedestrians, however, can have a contrary effect for cars due to its potential for reducing speeds. Low speeds below 20 mph have a significantly higher coefficient of pollutant production than above 30, though the coefficient after levelling off tends to increase gradually after 50 mph.[24] This effect is accentuated with high traffic density in areas with commercial uses where speeds come to a crawl. Since the grid plan is non-hierarchical and intersections are frequent, all streets can be subject to this potential reduction of average speeds, leading to a high production of pollutants. Greenhouse and noxious gases can be detrimental to the environment and to resident health.

Social environment and security[edit]

In his seminal study (1982) on livable streets that was conducted in neighbourhoods with a grid, Donald Appleyard showed that social networking and street playing degraded as traffic increased on a street. His research provided the groundwork for traffic calming and for several initiatives such as living streets and Home Zones, all of which are aimed at improving a street's social milieu. The amount of traffic on a street depends on variables such as the population density of the neighbourhood, car ownership and its proximity to commercial, institutional or recreational edifices. Most importantly, however, it depends on whether a street is or could become a through road to a destination. As a through road, it could sustain unpredictable levels of traffic that may fluctuate during the day and increase over time.

A key characteristic of the grid pattern is that any and all streets are equally accessible to traffic (non-hierarchical) and could be chosen at will as alternative routes to a destination. Cut-through driving, or shortcutting, has been resisted by residents.[25] Cities responded by making modifications to prevent it. Current recommended design practice suggests the use of 3-way intersections to alleviate it.[26]

The geometry of the normal, open grid is evidently unsuitable for protecting or enhancing the social environment of a street from the negative influence of traffic. Similarly, a 1972 ground-breaking study by Oscar Newman on a Defensible Space Theory described ways to improve the social environment and security of neighbourhoods and streets. In a practical application of his theory at Five Oaks, the neighbourhood's grid pattern was modified to prevent through traffic and create identifiable smaller enclaves while maintaining complete pedestrian freedom of movement. The positive outcome of these changes reinforces Appleyard's findings and the need to reduce or prevent through traffic on neighbourhood streets; a need that cannot be met with a typical, uniform, open grid.

The question of neighbourhood security has been a constant focus of research since Oscar Newman's work. New research has expanded the discussion on this disputed issue. A recent study[27] did extensive spatial analysis and correlated several building, site plan and social factors with crime frequencies and identified subtle nuances to the contrasting positions. The study looked at, among others, dwelling types, unit density (site density) movement on the street, culs–de-sac or grids and the permeability of a residential area. Among its conclusions are, respectively, that flats are always safer than houses and the wealth of inhabitants matters, density is generally beneficial but more so at ground level, local movement is beneficial, but not larger scale movement, relative affluence and the number of neighbours have a greater effect than either being on a cul-de-sac or being on a through street. It also re-established that simple, linear culs-de-sac with good numbers of dwellings that are joined to through streets tend to be safe. As for permeability, it suggests that residential areas should be permeable enough to allow movement in all directions but no more. The overprovision of poorly used permeability is a crime hazard. The open, uniform grid could be seen as an example of undifferentiated permeability.

A recent study in California[28] examined the amount of child play that occurred on the streets of neighbourhoods with different characteristics; grid pattern and culs-de-sac. The findings indicate that the open grid streets showed substantially lower play activity than the cul-de-sac street type. Culs-de-sac reduce perceived danger from traffic thereby encouraging more outdoor play. It pointed the way toward the development of hybrid street network patterns that improve pedestrian movement but restrict cut-through driving. Similar studies in Europe[29] and most recently in Australia[30] found that children's outdoor play is significantly reduced on through roads where traffic is, or perceived by parents to be, a risk.

Traditional street functions such as kids' play, strolling and socializing are incompatible with traffic flow, which the open, uniform grid geometry encourages. For these reasons, cities such as Berkeley, California, and Vancouver, British Columbia, among many others, transformed existing residential streets part of a grid plan into permeable, linked culs-de-sac. This transformation retains the permeability and connectivity of the grid for the active modes of transport but filters and restricts car traffic on the cul-de-sac street to residents only.

Pedestrian and bicycle movement[edit]

A 2X2 km square segment of the street network of Paris that often, and erroneously, is characterized as a grid. It shows the highly irregular city blocks and the range of street orientations, both common attributes of many historic cities

Two inherent characteristics of the grid plan, frequent intersections and orthogonal geometry, assist pedestrian movement. The geometry helps with orientation and wayfinding and its frequent intersections with the choice and directness of route to desired destinations. Street networks of old cities that grew organically, though admired for being picturesque, can be confusing for visitors but rarely for the original inhabitants (see plan). Similarly confusing to visitors are the plans of modern subdivisions with discontinuous and curvilinear streets. Change of street orientation, particularly when gradual or arbitrary, cannot be "mapped" in the mind. Impasses, crescents or cul-de-sacs frustrate the traveler especially when they are long, forcing an arduous retracing of steps.

Frequency of intersections, however, becomes also a disadvantage for pedestrians and bicycles. It disrupts the relaxed canter of walking and forces pedestrians repeatedly onto the road, a hostile, anxiety-generating territory. People with physical limitations or frailties, children and seniors for example, can find such walk challenging. For bicycles this disadvantage is accentuated as their normal speed is at least double that of pedestrians. Frequent stops negate the speed advantage and the physical benefit of bicycling and add to frustration.[citation needed] Intersections are not only unpleasant but also dangerous. Most traffic collisions and injuries occur at intersections and the majority of the injuries to pedestrians crossing with the right of way.

A dilemma arises from trying to meet important planning objectives when using the grid: pedestrianism, cost efficiency and environmental responsiveness. To serve pedestrians well, a rectangular configuration and high frequency of streets and intersections is the preferred route, which the orthogonal grid geometry provides. To reduce development costs and environmental impact, lower frequency of streets is the logical path. Since these two design objectives are contradictory a balance needs to be struck. Such balance has been achieved in leading modern projects such as Vauban, Freiburg and Village Homes, Davis. Both score high in pedestrian and bike mode share and, at the same time, in reducing negative development externalities. Their layout configurations represent a fusion of the classic grid plan with recent street network patterns.

Examining the issue of walkability, a recent comparison of seven neighbourhood layouts found a 43 and 32 percent increase in walking with respect to a grid plan and conventional suburban layout in a Fused Grid layout, which has greater permeability for pedestrians than for cars due to its inclusion of dedicated pedestrian paths. It also showed a 7 to 10 percent range of reduction in driving with respect to the remainder six neighbourhood layouts in the set, an environmental benefit.[31]

Safety[edit]

Perceived and actual safety play a role in the use of the street. Perceived safety, though perhaps an inaccurate reflection of the number of injuries or fatalities, influences parents' decision to allow their children to play, walk or bike on the street. Actual levels of safety as measured by the total number of collisions and the number and severity of injuries are a matter of public concern. Both should inform the layout, if the street network is to achieve its optimum use.

Recent studies have found higher traffic fatality rates in outlying suburban areas than in central cities and inner suburbs with smaller blocks and more-connected street patterns.[32][33] While some of this disparity is the result of distance from emergency medical facilities (hospitals are usually built in a fairly late stage of the development of a suburban area), it is clear[citation needed] that the lower speeds encouraged by the frequency of intersections decrease the severity of accidents occurring on streets within a grid plan.

An earlier study[34] found significant differences in recorded accidents between residential neighbourhoods that were laid out on a grid and those that included culs-de-sac and crescents. The frequency of accidents was significantly higher in the grid neighbourhoods.

Two newer studies examined the frequency of collisions in two regional districts using the latest analytical tools. They investigated the potential correlation between street network patterns and frequency of collisions. In one study,[35] cul-de-sac networks appeared to be much safer than grid networks, by nearly three to one. A second study[36] found the grid plan to be the least safe by a significant margin with respect to all other street patterns.

A 2009 study[37] suggests that land use patterns play a significant role in traffic safety and should be considered in conjunction with the network pattern. While all intersection types in general reduce the incidence of fatal crashes, four-way intersections, which occur regularly in a grid, increase total and injurious crashes significantly. The study recommends hybrid street networks with dense concentrations of T-intersections and concludes that a return to the 19th century gridiron is undesirable.

Stringent adherence to the grid plan can cause steep inclines since the topology of the land is not taken into account. This may be unsafe for drivers, pedestrians and bicycles since it is more difficult to control speed and braking, particularly in winter conditions.

Reconstruction and development[edit]

One of the greatest difficulties with grid plans is their lack of specialisation, most of the important amenities being concentrated along the city's main arteries. Often grid plans are found in linear settlements, with a main street connecting between the perpendicular roads. However, this can be mitigated by allowing mixed use development so that destinations become closer to home. Many cities, especially in Latin America, still successfully retain their grid plans. Recently, planners in the United States and Canada have revisited the idea of reintroducing grid patterns to many cities and towns.

Addressing[edit]

House numbering can be tailored to the grid...

QMRThe Fused Grid is a street network pattern first proposed in 2002 and subsequently applied in Calgary, Alberta (2006) and in Stratford, Ontario (2004). It represents a synthesis of two well known and extensively used network concepts: the "grid" and the "Radburn" pattern, derivatives of which are found in most city suburbs. Both concepts were self-conscious attempts to organize urban space for habitation. The grid was conceived and applied in the pre-automotive era of cities starting circa 2000 BC and prevailed until about 1900 AD. The Radburn pattern emerged in 1929 about thirty years following the invention of the internal combustion engine powered automobile and in anticipation of its eventual dominance as a means for mobility and transport. Both these patterns appear throughout North America. "Fused" refers to a systematic recombination of the essential characteristics of each of these two network patterns.[1][2][3]

It is shaped as a quadrant

Terminology and history[edit]

A diagram showing the street network structure of Radburn and its nested hierarchy. (Note: the shaded area was not built)

Modern urban planners generally classify street networks as either organic or planned. Planned networks tend to be organized according to geometric patterns, while the organic networks are believed to emerge from spontaneous, unorganized growth.

Architectural historian Spiro Kostof writes that "The word 'grid' is a convenient, and imprecise, substitute for 'orthogonal planning'. 'Gridiron' in the US implies a pattern of long narrow blocks, and 'checkerboard' a pattern of square blocks."[4] In addition to the right angle being a key characteristic, a second attribute of equal importance is its imputed openness and unconstrained expandability. Loosely interpreted, the term "grid" can be applied to plans such as the Vitruvian octagonal plan for an ideal city, resembling a spider web, or to plans composed of concentric circles. These are all grids in that a regularly spaced armature leaves recurring openings and that they could, conceivably, expand outward.

The emergence of the pure, rectilinear, orthogonal grid, or Hippodamian grid, is explained by the natural tendency of people to walk in a straight line, particularly in the absence of obstacles and on level land.[5] This intuitive explanation leaves the question of pre-grid and post grid non-rectilinear city patterns to be better understood, particularly those on plane territory such as Marrakech. Another potential influence may have been exerted by the second frequent user of city streets – horses. Horses also tend to move in a straight line, particularly at trotting, canter or galloping pace. When horses serve a city and draw chariots singly or in pairs, or, similarly, carts for a variety of transportation and processional functions, straight line travel becomes imperative; turns force a sluggish pace and cumbersome manoeuvres that reduce their efficiency of movement. The need for speed accentuates with city size; distances to the public functions at the centre increase and, consequently, the need for quick access intensifies. Speed in turn implies straight lines. It is plausible that the drivers for rectilinear layouts may have been man’s horses, mules and carts as much as man himself, spurred by the growth of settlements. The creation of the Radburn pattern is attributed to Clarence Stein but has a lineage of ideas that preceded it in Raymond Unwin and Barry Parker’s work that included the use of cul-de-sac and crescent street types. In contrast to the scarcity of records that obscures the original rationale for the grid, the reasons for the Radburn pattern has been articulated clearly in Stein’s writings and those of his predecessors.,[6][7]

Radburn" (after a place in New Jersey) now denotes a street network configuration. It signifies a departure from the strict orthogonal geometry and regularity of the grid and a distinct approach to laying out new districts. As a system, it can be described more accurately as a "cellular" network that has a characteristic hierarchy of streets as distinct from identical streets intersecting at regular intervals. Its derivatives and idiosyncratic imitations are often characterized as "cul-de-sac and loop" patterns highlighting the distinguishing street types that are used systematically in this network. A second term equally uncharacteristic is "suburban". This association of a pattern with a location is inaccurate and unintentionally misleading: entire early cities such as Cairo and Fez are structured on this pattern whose newer suburbs follow the grid reversing the urban/suburban relationship. "Suburban" is also devoid of geometric descriptors of the pattern. These shorthand expressions conceal the variety of patterns that emerged in the 20th century that are decidedly neither grids nor "Radburn"[8] and the "system" aspect of the pattern. The "loop and lollipop" label may be a more applicable descriptor of later interpretations of the Radburn model that appear to lack structure and to overlook key elements of the original concept such as its emphasis on pedestrian priority, for example. The pattern’s systematic use of the cul-de-sac and loop is decidedly linked to automotive mobility as a means of controlling and guiding its flow. The Radburn pattern is a complex system; more than a series of identical orthogonal city blocks in a linear progression. It rests on a functional program plus an intentional picturesque aesthetic: it avoids straight lines, limits four-way intersections and shuns repetitive blocks all of which enhance its picturesque imagery.[9] To facilitate the discussion, the name "Radburn-like" or "Radburn-type" will be used in the subsequent sections.

Criticisms of the prevailing network patterns[edit]

One of several streets of the grid that was applied to the hilly site of Piraeus.

A street in the Medina of Marrakech, showing the "wall" effect of agglutinated buildings and the absence of lower floor windows.

The two dominant network patterns, the grid and Radburn, have been debated by planners, transportation engineers and social observers on grounds that include issues of defence, aesthetics, adaptability, sociability, mobility, health, safety, security and environmental impact.

Defence, Aesthetics, Adaptability[edit]

The first known criticism of the grid was put forward on the grounds of defence that became irrelevant following the prevalence of the cannon (1500s). Aristotle argued that the old maze-like street pattern which preceded the grid, made it difficult for invading troops to find their way in and out of the city,[10] Alberti also expressed the same view 1500 years later and added the advantage of a superior visual effect of the organic pattern over the grid.[11] A second criticism was put forward most forcefully by Camillo Sitte on aesthetic grounds. He argued that grids lack variety and, consequently, are uninteresting and can become oppressive by their monotony.[12] This argument has been undermined first by the potential variety of grid dimensions that can be used in combinations such as appear in many city plans. More importantly, ground observation of cities shows that the mix of buildings and their varied street alignments as well as open spaces with their size variations coupled with constant redevelopment, suppress the monotony of the grid. Nonetheless, 20th century planners shunned pure grids and implicitly endorsed C. Sitte’s ideas on the need for a picturesque streetscape. This tendency is generally based on an intuitive aesthetic ground; that people dislike long open street vistas and prefer those that terminate.[13] Recent subdivision or town layouts such as Poundbury(1993), Seaside(1984) and Kentlands(1995) consciously avoided the homogenous grid and its open vistas. A further criticism of the grid focuses on its unsuitability for uneven, variegated terrain. Its application in sites such as Priene (350 BC), Piraeus (circa 400 BC), San Francisco (1776), Saint John, NB (1631) and others severely limits general accessibility by inadvertently introducing steep slopes or, in certain cases, stepped road sections and creates construction difficulties. In cities with intemperate climates this limitation is accentuated. Moving in a straight line uphill becomes arduous or, occasionally, impossible, particularly for non-motorized wheeled means of transport. A Radburn-type network inherently includes a variety of city blocks and terminating vistas and, consequently, pre-empts criticism centered on monotony and lack of end-closure. Its unconstrained geometry adapts easily to topographical irregularities and geographical features such as streams, woodlots and natural ponds. As neither the alignment nor the length of neighbourhood streets need to remain constant, this model gives planners considerable latitude in laying out a network.

Two newer aesthetic criticisms of the Radburn model emerged in the 1980s: the absence of a street "wall" or "enclosure" and the repetitiveness of housing unit forms as found in suburban districts. Both these criticisms can be understood as a misapplication of aesthetic norms on socio-economic outcomes.[dubious – discuss] The spaciousness of housing developments at the city’s edge echoes the spaciousness of contemporary houses and are both driven not by aesthetic intent but by economic prosperity.[citation needed] Judging the visual outcome of prosperity using historic streetscape criteria of cities with a different socioeconomic makeup would make the verdict predictable and practically meaningless. Moreover, the "street wall" and "enclosure" criticism of the Radburn pattern applications are undermined by observation of city districts new and old. Close examination would reveal that these spatial qualities are inextricably linked to housing unit and population density as well as construction technology and are not necessarily the outcome of a street pattern: The higher the habitation density of the street (and town) the closer and taller the buildings have to be to accommodate more people. A street pattern does not induce either unit density or the visual wall effect. For example, in earlier cities with labyrinthine street layouts, analogous to some contemporary suburban districts, residential buildings were agglutinated creating an entire perimeter wall around the city block with few perforations for reasons of security, safety and a heightened sense of privacy, not streetscape aesthetic. Conversely, early founded cities in NA, where land was almost free but construction costly, are depicted with generous lot dimensions and very small houses on them (e.g. Salt Lake City) that created a weak "enclosure" vertically and horizontally. At both ends of the streetscape scale, very proximate and very sparse buildings, socio-economic factors drive the outcome.

Surveyor's plan of Salt Lake City, circa 1870s - an example of a uniform square grid

A straight street of a grid pattern in a 1950s suburb exhibiting low density, single family detached housing

Regarding repetitiveness of housing form, ground observation shows no relation to street pattern. Homogeneity correlates better with methods of production. Early agglutinated housing forms as in Pompeii and Tunis, with vastly different street patterns, presented no face on the street by which design differences could be discerned; plain and luxurious houses had the same nondescript, blank street face. In recent times, older streets of more recent cities with a grid show considerable replication, based on vernacular and pattern books, as do newer streets on the fringe, based on industrialization. What has impacted the urban landscape appreciably is the scale of production: many single operators in earlier periods with small yearly output versus few large corporations by mid-20th century with high annual production volumes. Inevitably, the larger the operation is, the greater the economies of repetition are. Similar house models can be found not only in the same subdivision but across states and even nations. For example, veterans housing that was built in Canada consists of two or three models that were repeated in neighbourhoods and across the country. The most impressive effect of large scale production is starkly visible in Levittown, New York (1947) and in social housing projects, where the State also aims at economies of scale. In the case of early Huguenot settlements, sameness of houses on identical grid patterns was pursued as a means of expressing the social equality of all inhabitants – a community goal.[14]

Housing Unit Density[edit]

Derivatives and variations of the Radburn street network pattern, collectively "the suburbs", have been criticized on the grounds of their relative low density. The low density criticism appears to be based on a historical coincidence mistaken for causality: most low density housing developments occurred in the 20th century at the periphery of existing cities after 1950 and intentionally incorporated cul-de-sac or looped streets (Radburn-inspired street types) regularly. By contrast, dense development occurred earlier (and continues) in city central areas most of which were laid on a grid pattern in the 19th century or earlier. This topological coincidence of pattern and density can be easily mistaken as a causal relationship. Radburn (1929), a suburb, was built at a density (19 persons per acre) higher than subsequent suburbs such as Kentlands (14 persons per acre) that were laid out on a grid-type pattern.[15] Also, many early grid-plan towns and suburbs such as Windermere, Florida, Dauphin, Manitoba, and St. Andrews, New Brunswick exhibit grid layouts and very low densities. Conversely, incidental cul-de-sac and crescent streets in central areas show high densities. Examples of unusual, unconventional associations of density and street type demonstrate that street patterns are coincidentally, not causally, related to housing density. Any given street pattern can be built at a predetermined density.

Security[edit]

Questions have been raised about the potential effect that the street patterns of a neighbourhood may play a role in the frequency that its homes are targets of theft and property damage. These questions were prompted by the apparent higher concentration of such events in certain neighbourhoods over the general average. This potential connection has been debated extensively. Factors such as sample size, analytical methods and the inclusion or omission of socio-demographic profiles of offenders, victims and neighbourhoods can confound the research outcomes. Yet some tentative correlations have been discerned.

Experiments are rarely possible in existing neighbourhoods where the street pattern, the properties and the residents are given and inalterable. One such rare experiment, however, was tried in Five Oaks, Dayton, Ohio. A "troubled" neighbourhood’s street pattern was converted from the regular grid to an interrupted grid resembling the Radburn pattern. The transformed layout was made discontinuous for cars but continuous for pedestrians through the use of connected cul-de-sacs. Following the change, the drop in antisocial incidents was substantial and immediate suggesting that the Radburn-like pattern contributed to it since all other factors remained practically unchanged.[16] Observational studies rest on cross-sectional statistical analysis of neighbourhoods to derive potential correlations between street patterns and the level of antisocial incidents. One such study [17] concluded that:

a) flats are always safer than houses and the wealth of inhabitants matters;

b) density is generally beneficial but more so at ground level;

c) local movement is beneficial, larger scale movement not so;

d) relative affluence and the number of neighbours has a greater effect than either being on a cul-de-sac or being on a through street.

e) As for permeability, it suggests that residential areas should be permeable enough to allow movement in all directions but no more. The over-provision of poorly used permeability is a crime hazard.

It also re-established that simple, linear cul-de-sac streets with good numbers of dwellings that are joined to through streets tend to be safe. Of the five concluding observations three are unrelated to network pattern, indicating the overriding role of socio-economic factors. The consensus among researchers is that streets patterns in themselves cannot be seen as crimino-genic. The genesis of crime rests elsewhere. Of the factors that assist the intent for crime, however, unconstrained permeability appears the most influential. The Radburn pattern restricts permeability while the uniform grid enables it.

Transportation, traffic and their effects[edit]

More significant criticisms of the grid and the Radburn patterns were put forward based on the new urban transportation context of unprecedented levels of motorised mobility that raises issues of traffic congestion, collisions, accessibility, connectivity, legibility for pedestrian and driver, noise disturbance, car travel extent, air and water pollution and Greenhouse Gas emissions . The importance of these criticisms rests on judging the functional adequacy of alternative networks regarding these aspects. Dysfunctional systems could entail heavy economic and social burdens that may be avoidable.

Mobility and congestion[edit]

The introduction of mechanized personal transport in large numbers during the 20th century tested every existing network’s characteristics and their capacity to function satisfactorily for mobility and for city living in general. And since most cities where the motorcar first appeared had a grid layout,(e.g. New York, Chicago and London) it was inevitably the first network pattern to experience its impact.

The grid’s emergence in a pedestrian world, in which wheeled traffic of horse-drawn carts was limited, along with its extensive replication, attest indirectly to its functional adequacy for pedestrian movement. The new question about its adequacy for serving motorized movement and for serving both prime modes, motorized and non-motorized in combination, continues to be debated.

Early signs of a potential drawback of the orthogonal grid layout in serving wheeled traffic were discovered in Pompeii, Italy;[18] at certain intersections left turns were prohibited and some streets or sections of others were decreed one-way. Contemporary traffic engineering recommends these measures to decrease congestion and improve flow in Centertown grids and have been applied extensively. It is worth noting that, the Pompeii restrictions occurred at horse and wagon speeds in the range of 5 to 10 km/hr, far below car speeds. Definitive proof of this deficiency, however, appeared 20 centuries later, when speeds and volumes of traffic reached critical thresholds and analysis of large numbers of data became computerized. However, a new complicating factor surfaced through adaptation.

Operational methods to control the flow of traffic and avoid collisions were introduced and grew steadily in sophistication, from traffic signs to computer-controlled, time-orchestrated systems. While the necessity of these adaptations provides practical proof of the grid’s inadequacy to serve motorized transport unaided, their introduction made theoretical proof harder. Highly advanced computer modeling of traffic flows overcame this difficulty. Another complicating factor in the early stages of motorization was the absence of a characteristic and typical alternative network pattern for a comparative analysis. Unlike the clear geometry of the grid, idiosyncratic, peculiar and site specific layouts, that have no obvious elements of a ‘pattern’ or ‘stencil’, cannot be accurately described and generalized. The only distinguishing element of current alternatives is their loose dendrite configuration, which is inherently hierarchical, that could be contrasted with the grid’s inherent absence of hierarchy. Since in built districts neither of these networks appears in pure form, another level of complexity is introduced that tempers the certainty of analytical findings.

Of two studies that have attempted the comparison between "Radburn-type" and "grid-type" networks, one is based on two hypothetical layouts for a specific site and the second on an existing district layout and two hypothetical overlays. The relationship of congestion to layout geometry and density have been tested using computer-based traffic modeling. The first study, reported in 1990[19] compared the traffic performance in a 700-acre (2.8 km2) development that was laid out using two approaches, one with a hierarchical street layout that included cul-de-sac streets and the other a traditional grid. The study concluded that the non-hierarchical, traditional layout generally shows lower peak speeds and shorter, but more frequent intersection delays than the hierarchical pattern. The traditional pattern is not as friendly to the long trips as the hierarchical but friendlier to short trips. Local trips in it are shorter in distance but about equivalent in time with the hierarchical layout.

A second extensive comparative traffic study [20] of a subdivision about 830 acres (3.4 km2) tested three network models. It also tested the resilience of the layouts to an increased traffic load generated by higher residential densities. This study confirmed the previous findings that up to a density of 70 ppha[clarification needed] (including jobs), which is above the average range of subdivision densities of 35 to 55 ppha, the grid layout had a marginally higher or equal delay per trip to the Radburn-type network. At a 90 ppha, the conventional pattern showed marginally higher delay per trip than the grid. This outcome suggests that within the normal range of residential subdivision densities the grid has a slight disadvantage, but under very dense conditions the slight advantage reverses in favour of the grid-type and that both may be subject to improvement.

Traffic Safety[edit]

A traffic circle applied to a four-way intersection as a means of improving its safety. This device, with a proven record of collision reductions and traffic flow improvement, turns the cross-intersection into four virtual three-way intersections.

The grid’s traffic safety performance in comparison to other network types has been studied extensively and a general consensus is emerging both in theory and practice that, in general, it is the least safe of all currently used network patterns. A 1995 study[21] found significant differences in recorded accidents between residential neighbourhoods that were laid out on a grid and those that included cul-de-sacs and crescents. The frequency of accidents was measurably higher in the grid neighbourhoods.

Two subsequent studies examined the frequency of collisions in two regional districts using the latest analytical tools. They investigated the potential correlation between street network patterns and frequency of collisions. In one 2006 study,[22] cul-de-sac networks appeared to be much safer than grid networks, by nearly three to one. A second 2008 study[23] found the grid plan to be the least safe by a significant margin with respect to all other street patterns in the set. A 2009 study [24] suggests that land use patterns play a significant role in traffic safety and should be considered in conjunction with the network pattern. While land use matters, intersection types also affect traffic safety. Intersections in general reduce the incidence of fatal crashes due to reductions in speed, but four-way intersections, which occur regularly in a grid, increase total and injurious crashes significantly, all other things being equal. The study recommends hybrid street networks with dense concentrations of T-intersections and concludes that a return to the 19th century gridiron is undesirable.

Improved traffic safety has been shown to result from modifications to existing neighbourhoods laid out on a grid, indirectly suggesting its weakness with respect to safety. One study of the impacts of modifications[25] found that Area-wide urban traffic-calming schemes reduce the number of injury accidents by about 15 percent on average. The largest reduction of accidents is found for residential streets (about 25 percent); a somewhat smaller (about 10%) reduction is found for main roads.

Vulnerable road users[edit]

Following the introduction of motorized transport, pedestrians do not fare well in cities. Their space and freedom of movement has gradually been curtailed and the risk of injury increased. They are now seen and studied as Vulnerable Road Users (VRU) along with bicycle riders because of their overwhelming disadvantage in the case of a collision.

Pedestrians experience stress and delay at every intersection, particularly when their mobility has been compromised either temporarily or through the aging process. A delay is unwelcome to pedestrians given that their slow speed and limited range of reach; the more frequent the intersections the higher the delay. Given the grid’s origin as a network for pedestrian movement, it is important to understand how it serves pedestrians when it must synchronously serve vehicular traffic. A 2010 study concluded that of seven network patterns, including the Radburn-type pattern, the grid was the least safe for vulnerable road users such as pedestrians and bicycles.[26]

Legibility

Legibility[edit]

A 2X2 km square segment of the street network of Paris with an approximate scale bar. It shows the highly irregular city blocks and the range of street orientations, both common attributes of many historic cities

Uniform grids with fixed cardinal directions can be mapped as easily on paper as on the mind. This quality — legibility — assists people in finding destinations and prevents the apprehension of being lost. However, this benefit is felt more by visitors to a district than by its residents. Many historic cities with labyrinthine plans, particularly in the medieval period and in the Islamic-Arab world, cause no anxiety to their permanent residents. (Some visitors, equipped with maps, see them as a delightful journey of discovery.) Many parts of Paris, France, for example, exhibit a highly irregular block dimensions and a wide range of street orientations not easily grasped by visitors. Residents quickly acquire many perceptual clues of direction and position without ever seeing printed maps of their domains and, in earlier times, without even the benefit of street signs. Legibility can be an advantage but it is not a necessary condition for a neighbourhood or a town to function well for its residents. While the uniform grid offers utmost legibility, mutated grids and other patterns can function adequately for finding directions.

Walkability[edit]

Walkability, a neologism, refers to those characteristics of an area which enable or hinder one's ability to walk around. More specifically, "walkable" means close; barrier-free; safe; full of pedestrian infrastructure and destinations; and upscale, leafy, or cosmopolitan.[27] Of these characteristics some are related to the street network configuration, such as "close" and "pedestrian infrastructure" while others relate to land use and level of amenity such as destinations and sidewalks. The uniform grid’s inherent high frequency and openness makes closeness easily achievable as the chosen routes can be direct. In its central city expression blocks are generally short and equipped with a sidewalk on each side. Suburban grids, however, often depart from the classic square block and include long orthogonal blocks and sidewalks only on one side or none at all. Similarly contemporary versions of the classic Radburn and Hampstead Garden Suburb do not always include pedestrian linkages that were present in the original. They too lack sidewalks, mostly to reduce costs but also on the assumption that resident traffic is low enough for the road pavement to be shared by all without risk.

Published studies examined the relative connectivity of neighbourhoods built following the grid stencil or the Radburn-type pattern. A 1970 study compared Radburn to two other communities, one, Radburn-type (Reston, Virginia) and a second, a nearby unplanned community. It found that 47% of Radburn’s residents shopped for groceries on foot, while comparable figures were 23% for Reston and only 8% for the second community. A 2003 study also compared Radburn (1929) to a neo-traditional development (1990). It found that the rates of connectivity differed with the destination. Shopping was considerably more direct and closer in Radburn while the elementary school was just as direct in both but at a marginally longer distance in Radburn. Accessibility to the park was virtually the same.[28] Overall, walkability was marginally better in the Radburn neighbourhood.

A 2010 study, compared eight neighbourhoods of which four followed the grid network rules while the remainder adhered to the Radburn-type network structure. Connectivity, values ranged between 0.71 to 0.82, with the upper limit being 1.00. The grid-like set had two samples above the 0.76 average and one below, while the Radburn-type set had one above average and two below. The amount of walking did not correlate well with the connectivity values indicating that other factors were at play.[29] Walking correlated better when the additional pedestrian infrastructure, independent paths was included. These results confirmed previous findings that while connectivity, the essential characteristic of the grid, is a necessary condition for walkability it is not sufficient by itself to entice walking.

A third study compared seven neighbourhoods by examining their walking and driving activity as an indicator or a network’s propensity to entice walking. Using the agent-based modeling method it calculated the amount of walking under identical land use conditions. The traditional uniform grid, two Radburn-type patterns and one neo-traditional grid had lower levels of walking activity than a second version of the neo-traditional grid and the fused grid. Overall the Radburn-type networks had lower average walking scores and higher driving activity.[30] These results show that the influence of the street network on walkability is clearly evident but also dependent on the specific characteristics of its geometry.

Transit accommodation[edit]

Although the grid was introduced long before any system of public transit would become necessary or available, its strict regularity provides sufficient flexibility for mapping transit routes. By contrast, derivatives of the Radburn-type network, particularly the non-cellular and strictly dendrite variety, are inflexible and force transit routes that are often long and circuitous resulting in an inefficient and costly service.

Environmental Issues[edit]

Until the second half of the 20th century, the prime purpose of linking people to places has also been the prime criterion for judging a network’s performance. New criteria surfaced when questions about the impact of development on the environment were raised. In that new context, a network’s land consumption; its adaptability to the land’s natural features; the degree of water impermeability it introduces; whether it lengthens trips and how it affects the production of greenhouse gases constitute part of a new set of criteria.

Adaptability[edit]

Typical, uniform grids are unresponsive to topography. Priene’s plan, for example, is set on a hill side and most of its north-south streets are stepped, a feature that would have made them inaccessible to carts, chariots and loaded animals. Cities established more recently have utilized a similar approach to Priene's, for example: San Francisco, Vancouver, and Saint John, New Brunswick. In a modern context, steep grades limit accessibility by car and more so by bicycle, on foot, or wheelchair, particularly in cold climates. The strict orthogonal geometry forces roads and lots over creeks, marshes and woodlots, thus disturbing the local ecology. It is said of the 1811 NY grid plan that it flattened all obstacles in its way. By contrast, the unconstrained geometry of the Radburn-type networks provides sufficient flexibility to accommodate natural features.

Land consumption and conservation[edit]

Depending on the choice of street pattern and the cross section of the street space, streets consume an average 26% of the total developed land.[31] They can range from 20% to over 40%. For example, the Portland grid consumes 41% of the development land in street Right-of-Ways (ROW). At the low end of usage, Stein’s Radburn neighbourhood uses about 24% of the total. Villages and towns with narrow streets (2 to 3 m wide) consume much less.

Actual layouts of specific districts show variability within that range due to site-specific conditions and network pattern idiosyncrasies. Land taken up by streets becomes unavailable for development; its use is inefficient since it stays empty for most of the time. Were it to be developed, less land would be required for the same number housing units, resulting in lowering the pressure to consume more of it.

A 2007 study [32] compared alternative layout plans for a 3.4 square kilometre subdivision and found that the traditional grid layout had 43 percent more land dedicated to roads than the conventional Radburn-type network.

Water cycle and water quality impacts[edit]

All new development, irrespective of its network pattern, alters the pre-existing natural condition of a site and its ability to absorb and recycle rain water. Roads are a major factor in limiting absorption by the sheer amount of impermeable surfaces they introduce. They affect water usability by the generation of road surface pollutants that end up downstream making it unfit for direct use.

The grid’s inherent high street and intersection frequencies produce large areas of impermeable surfaces in street pavement and sidewalks. In comparison to networks with discontinuous street types, that are characteristic of the Radburn pattern, grids can have up to 30% percent more impermeable surface attributable to roads. One study compared alternative layouts on a 155 ha (383 acre) site and found that the grid-type layout had 17% more impermeable surface area in total compared to the Radburn-type layout.

Vehicle Kilometres Traveled and Exhaust Emissions[edit]

Emissions from all transportation account for about 30% of the total from all sources and personal car use amounts to about 60% percent of that share that translates to about 18% percent of the total GHG production. Three factors that affect emissions from personal travel relate to network configuration and function: a) trip length b) speed of travel c) propensity for congestion. Studies have shown that Radburn-type networks could add up to 10 percent to the length of local, short trips. As was seen earlier under congestion, grid-type patterns induce longer trip times that are primarily due to stops at the characteristic and frequent four-way intersections.

A 2007 study [33] compared total traveled kilometres and total estimated emissions. Regarding the trip length, it confirmed previous studies by finding a 6% increase in local VKTs in the Radburn-type layout. The emissions comparison excluded CO2 and focused on three noxious (criteria) gases. Totalling the estimated cost of these emissions for ease of comparison, it found a 5% increase in costs for the conventional Radburn type layout.

Development and Lifecycle costs[edit]

With the prevalence of motorized mobility, street infrastructure represents the single largest component of capital outlays for building a new neighbourhood. Until the end of the 19th century most city streets were unpaved, had no drainage sewers, few were lit, and hardly any had signage. Also, the majority were narrow by contemporary standards, frequently without sidewalks. Consequently, they consumed few resources for construction and maintenance. By contrast, current street design standards necessitate a large investment for construction and significant city budget allocations for their maintenance. A 2008 engineering study compared network patterns for the same district and found that the traditional, modified grid network (TND) pattern had about 46% higher costs for road infrastructure compared to the Radburn-type of the existing layout.

These figures exclude the opportunity cost attributable to land that becomes unavailable for private use. The Radburn-type layout has approximately 30% less land dedicated to roads than the Neo-traditional layout. When accounting for this land and using a cost of $162,000 per hectare ($40,000/acre (2007 Dollars), land costs for roadways increase the relative cost for road infrastructure from a difference of 46% to 53% between the two layouts.

The same study examined the lifecycle costs for the two network options and found that, similar to the capital costs, roads remain the key cost component of a community when accounting for on-going operations, maintenance and replacement costs.

Summary of positive attributes[edit]

In judging the two currently disputed network concepts it would appear that neither has all the requisite elements needed for adequately responding to the new urban transportation context of extensive motorized mobility. The Radburn pattern fares better overall since it was consciously designed "for the motor age". Similarly, the weaker overall performance of the grid can be understood as innate, given its origin in a predominantly pedestrian world.

Advantages of a Radburn-like pattern:

less costly to construct and maintain

more flexible in adapting to the topography

greater ground permeability

lower trip delay

safer for cars and pedestrians

more picturesque

may provide a more sociable environment, particularly for children

may be more secure, all other factors being equal

Advantages of a grid-like network:

reduces local distances due to its frequency of intersections

more walkable

accommodates transit easily

more legible, when it maintains the orthogonal directions

easy to lay out as city blocks and plots

The need for an alternative[edit]

An adaptation to the grid street network (closure) that prevents through car traffic while permitting full access to pedestrians and bicycles

To function well, a contemporary network must include these advantages from the contrasting patterns thus reducing frictions and conflicts in urban environments. The need for an alternative has been evident since the middle of the 20th century for practical and theoretical considerations. In practice, in the second half of the 20th century citizens of many American and European cities have protested the intrusion of through traffic in their neighbourhoods. Its side-effects were unwelcome as being detrimental to peace, tranquility, health and safety. In response, cities introduced an armoury of controls to ensure that residential districts retained a high standard of life quality. Among these controls were one-way streets, closures, half-closures, traffic circles, and a liberal use of stop signs.[34] These measures being improvised retrofits implied the need for a network pattern in which techniques such as these would be obviated by innovative design. On the theoretical level, planners analysed the conflicts caused by the new urban mobility, proposed alternative schemes and, in some cases, applied them. Alexander proposed (1977) a genetic code of 10 "patterns" [35] which, when combined would resolve identified conflicts and would produce a convivial, gratifying district milieu. A central idea among them is a traffic impermeable neighbourhood area of about 10 ha, reminiscent of the Radburn plan principle but smaller in size. Doxiadis emphasized the importance of mobility and designed a large orthogonal grid (2 km by 2 km)of arterials to expedite circulation, as seen in Islamabad. He also recognized the need to separate "man from machine"[36] and introduced traffic impermeable neighbourhoods also generally resembling the Radburn plan.

The Fused Grid model[edit]

District with four neighbourhoods and mixed use zone, showing the twin connectors

Based on these sets of issues, the identified advantages of alternative patterns and the ideas of 20th century theorists, the Fused Grid assembles several elements from these precedents into a complete stencil. Just as the grid stencil and the Radburn pattern did, it sets up a geometric structure that exhibits the key characteristics of a functioning system. It consists of a large-scale open grid of collector streets, carrying moderate speed motorized traffic. This grid forms precincts (quadrants, neighbourhoods) that are normally about 16 ha (40 acres) in size (400 m by 400 m). Within each precinct, the layout uses crescents or cul-de-sacs or a combination of both to eliminate through traffic. In addition, a continuous open-space and pedestrian path system provides direct access to parks, public transit, retail and community facilities. Residents can cross a quadrant block on foot in about five minutes. The most intensive land uses such as schools, community facilities, high-density residential uses, and retail are located in the center of the plan, reached by twinned roads which connect longer, district destination points.

This synthesis of inherited network traditions and ideas is accomplished through the application of two practical means: a rectilinear, orthogonal geometry, a key characteristic of the grid, and the use of two street types that have generally been associated with the Radburn-type subdivisions.

A diagram showing the nested hierarchy of roads in the Fused Grid transportation network

The orthogonal geometry serves two purposes: a) to enhance the navigability of the network structure particularly at the district and regional scale. This is important at car speeds where decisions about destinations and turns have to be made promptly. b) to maintain a good level of safety at road intersections, as recommended by traffic engineering manuals. The grid’s second essential characteristic, connectivity, is recaptured through a third element that completes the "system" – pedestrian-only connectors between regular streets that are intended for all movement modes. These connectors (paths) are typically routed through open spaces that occupy central points in a neighbourhood cell. Thus the neighbourhood street network comprises a mixture of streets; some pedestrian dominant and others car dominant. A fourth element is the nested hierarchy of streets that distinguishes between connectivity and permeability at the neighbourhood level. This idea reflects the fact the longer the linked destinations the higher the level of mobility must be. A dendrite configuration, such as a river, takes progressively wider expanses of land to accommodate the flow. A nested hierarchy[37] on the other hand distributes the flow at each volume level to alternative paths. The complete system, though it may appear unfamiliar, is composed of entirely familiar and extensively used elements in contemporary development.

Proof of concept[edit]

An approved Community Development Plan in Calgary, Alberta that is based on the Fused Grid model

The model has been applied in two new communities, one in Stratford, ON and the other in Calgary, Alberta. The potential merits of the concept so far have been tested through research; site observations or measurements will await full built out. The aspects of the model that have been tested correspond to the key criteria of performance, listed above, such as mobility, safety, cost and environmental impact.

Mobility[edit]

A study on the transportation impacts of the fused grid [38] asserted through comparative analysis using computer-based traffic modeling that the fused grid produces the least total delay in all four density scenarios tested and performed progressively better as the density increased. Taking the fused grid as 100 (base), the delay was 32% more for the conventional Radburn-type pattern and 27% higher for the grid-type pattern. At the next higher density level the difference between patterns increased and they were correspondingly 100 (fused grid), 152 (Radburn-type) and 126 (grid -type). Traffic modeling shows the potential of the fused grid to reduce time delay during peak hours and, therefore, congestion.

Traffic Safety[edit]

In a fused grid, three-way intersections are more common than four-way, which have been shown by traffic studies to be less safe.[24][39][40] One study found that for each probable collision in the fused grid there would be 2.55 collisions in a standard grid, 2.39 in a Dutch SRS[clarification needed], 1.46 in a cul-de-sac layout and 0.88 in a 3-way Offset layout.[41]

Walkability[edit]

An extensive study of neighbourhoods based on geo-coded trips to local destinations found that a Fused Grid type of layout increases home-base walking trips by 11.3% in comparison to the conventional grid and it is associated with a 25.9% increase in the odds that residents will meet the recommended physical activity levels. Its 10% increase in relative connectivity for pedestrians is associated with a 23% decrease in vehicle kilometres of local travel. [42]

A second study compared seven neighbourhoods of different street network layouts for the daily travel patterns including the amount of walking that occurred. It found that the fused grid had considerably more walking activity. The set of network patterns included two versions of the traditional grid, two versions of post-war suburbs, two versions of the Traditional Neighbourhood Development (i.e. modified grid) and the Fused Grid. The lowest amount of walking was found to happen in one of the post-war conventional subdivision. Setting this as the base (100) for the purpose of comparison, the two classic grids registered 11%, one conventional subdivision 109%, one TND neighbourhood 108%, the second TND 137% and the Fused Grid 143%.[43] In terms of the total distance walked, the Fused Grid registered 23% larger distance than the lowest of the seven in the set which was also reflected in the lowest amount of local driving.

The fused grid anticipates the location of convenience shopping and amenities at the periphery of the four-quadrant neighbourhood. In such a configuration any part of the neighbourhood is a five-minute walk to the periphery and a ten-minute walk across the entire neighbourhood. Closeness of destinations is inherent in the structure of the network. The same structure, based on 400 m intervals, coincides with current practices for transit route location. Consequently, the street network pattern, the anticipated land use distribution and the location of transit stops are all conducive to walking.

Health outcomes[edit]

Neighbourhood layouts may indirectly influence the health and wellbeing of residents through their effect on factors such as noise, air quality and physical activity. Noise levels and duration of exposure correlate with traffic volume and speed. According to a traffic analysis study[44] neighbourhood streets in the fused grid layout exhibit the lowest traffic volumes when compared to alternative layouts. By inference, low volumes imply lower duration of exposure to noise. Frequent turns in the streets (see drawing of approved development plan) result in speed reduction which lowers noise intensity. As a consequence of low traffic volumes, its residential streets show low air pollution levels.[30] The high walking levels registered by the fused grid layout, mentioned above, indicate the potential of increased physical activity.

In addition to these three factors that may impact on resident’s health - noise, air quality and physical activity - a fourth one, proximity to natural open spaces, has emerged as a significant contributor. Previous studies have confirmed the beneficial effect of frequent contact with nature and some have investigated the probable mechanism of the effect via stress abating biochemical processes,.[45][46][47][48] More recently, links were established to specific biota (microorganisms) found in nature and their direct influence on building immune system strength.[49] From these studies it can be inferred that a neighbourhood layout based on the fused grid model may confer these health and well-being benefits to residents because it incorporates green open spaces as integral parts of its pedestrian circulation network. Inclusion of green spaces is possible in any layout as an option; in the fused grid it is a necessary component of its configuration.

Site adaptability[edit]

The virtual grid mesh that underlies the fused grid network structure is expressed at 400 m intervals, five times the size of the traditional city block (about 80 m). At this scale there is greater flexibility to adapt the network elements to the topography and to specific site boundary constraints that are common in property configurations. Within the 16 ha quadrant, the discontinuous character of the streets and the possible combination of cul-de-sac and loop types provide sufficient latitude to the site plan designer to lay out an adapted version of the fused grid . There are at least 15 variations of the quadrant design that can be moulded to fit specific conditions. The site adaptability of the model has been demonstrated in the two approved layout plans.

Ground Permeability[edit]

One study [50] quantified the relative permeability of three alternative site plans for the same site. The analysis results show that the impermeable areas of the three layouts - assuming roads, building foot prints and sidewalks to be impervious surfaces - ranged from 34.7% of Fused Grid to 35.8% of the conventional suburban to 39% of the grid-like pattern. Streets were the single most influential factor in the amount of the water runoff. They account for an impermeable surface which is up to three times that of the building footprint. Of the total impermeable area in the three layouts the portion attributable to streets ranges from 48 to 65 percent with the fused grid occupying the low end. The reduction in street length and the systematic use of open spaces as structural elements of the layout increase the potential of greater water permeability in the Fused Grid.

Development and Municipal costs[edit]

A study compared the cost efficiency of three network patterns in improving the traffic performance of a district. It first established the cost of the network system of each before evaluating the efficiency ratio for the resulting traffic improvement.[51] The analysis showed that the most significant capital cost of development is for roads. The conventional layout has the lowest capital costs for roads followed by the Fused Grid at 12% higher and the Neo-traditional (grid) layout at 46% higher. When considering the opportunity cost for land dedicated to Right-of- Ways (ROW), the Fused Grid allocated 9% more land to roads than the conventional while the Neo-traditional grid allocated 43% more. Similar to capital costs, roads remain the key cost component of community development after accounting for on-going operations, maintenance and replacement costs.

The study showed that there are significant differences in costs related to travel delay for the total road network particularly at the desirable transit-supportive densities. The delay costs incurred by the conventional layout are 12% higher than the fused grid followed by the Neotraditional grid at 3% higher. The conventional layout is less cost efficient than the fused grid network since they have similar infrastructure costs but the latter delivers significant savings in travel time costs. The travel time benefits of the Neo-traditional grid layout are disproportional to the required infrastructure investment. The obvious benefits of saving time for pedestrians and the enticement of more walking have not so far been monetized.

Applications of the Fused Grid[edit]

Retroactive application of the fused grid model can be seen in the centres of old European cities, such as Munich, Essen, and Freiburg and in newer railway towns or suburbs such as Vauban, Freiburg and Houten in theNetherlands. In most of these cases, acknowledging the constrains of an existing build environment, the key fused grid characteristic of a traffic impermeable centre is evident along with the primacy and continuity of pedestrian-only links to the remainder of the inherited street system. The Fused Grid is promoted in Canada by the Canada Mortgage and Housing Corporation.

A similar debate has also been taking place in Europe and particularly the UK, where the term filtered permeability[52] was coined to describe urban layouts which maximise ease of movement for pedestrians and cyclists, but seek to restrain it for motor vehicles.

QMRPermeability or connectivity describes the extent to which urban forms permit (or restrict) movement of people or vehicles in different directions. The terms are often used interchangeably, although differentiated definitions also exist (see below). Permeability is generally considered a positive attribute of an urban design, as it permits ease of movement and avoids severing neighbourhoods. Urban forms which lack permeability, e.g. those severed by arterial roads, or with many long culs-de-sac, are considered to discourage movement on foot and encourage longer journeys by car. There is some empirical research evidence to support this view.[1]

Permeability is a central principle of New Urbanism, which favours urban designs based upon the ‘traditional’ (particularly in a North American context) street grid. New Urbanist thinking has also influenced Government policy in the United Kingdom, where Department for Transport guidance Manual for Streets says:[2]

Street networks should in general be connected. Connected or ‘permeable’ networks encourage walking and cycling and make places easier to navigate through.

perfect quadrants are more permeable

QMRA city block, urban block or simply block is a central element of urban planning and urban design.

A city block is the smallest area that is surrounded by streets. City blocks are the space for buildings within the street pattern of a city, and form the basic unit of a city's urban fabric. City blocks may be subdivided into any number of smaller land lots usually in private ownership, though in some cases, it may be other forms of tenure. City blocks are usually built-up to varying degrees and thus form the physical containers or 'streetwalls' of public space. Most cities are composed of a greater or lesser variety of sizes and shapes of urban block. For example, many pre-industrial cores of cities in Europe, Asia and the Middle-east tend to have irregularly shaped street patterns and urban blocks, while cities based on quadrant grids have much more regular arrangements

QMRGrid plan[edit]

In most cities of the world that were planned, rather than developing gradually over a long period of time, streets are typically laid out on a grid plan, so that city blocks are square or rectangular. Using the perimeter block development principle, city blocks are developed so that buildings are located along the perimeter of the block, with entrances facing the street, and semi-private courtyards in the rear of the buildings.[1] This arrangement is intended to provide good social interaction among people.[1]

Since the spacing of streets in grid plans varies so widely among cities, or even within cities, it is difficult to generalize about the size of a city block. However, as reference points, the standard square blocks of Portland, Houston, and Sacramento are 260 by 260 feet (79 m × 79 m), 330 by 330 feet (100 m × 100 m), and 410 by 410 feet (120 m × 120 m) respectively (to the street center line). Oblong blocks range considerably in width and length. The standard block in Manhattan is about 264 by 900 feet (80 m × 274 m); and in some U.S. cities standard blocks are as wide as 660 feet (200 m). The blocks in Edmonton, Canada are 330 by 560 feet (100 m × 170 m).[2] The blocks in central Melbourne, Australia, are 330 by 660 feet (100 m × 200 m), formed by splitting the square blocks in an original grid with a narrow street down the middle.

Many world cities have grown by accretion over time rather than being planned from the outset. For this reason, a regular pattern of even, square or rectangular city blocks is not so common among European cities, for example. An exception is represented by those cities that were originally founded as Roman military settlements, and that often preserve the original grid layout around two main orthogonal axes. One notable example is Turin, Italy. Following the example of Philadelphia, New York City adopted the Commissioners' Plan of 1811 for a more extensive grid plan. By the middle of the 20th century, the adoption of the uniform, rectilinear block, subsides almost completely and more picturesque layouts prevailed, with random sized and either curvilinear or non-orthogonal blocks and corresponding street patterns.

In much of the United States and Canada, the addressing systems follow a block and lot number system, in which each block of a street is allotted 100 building numbers.

Grids are quadrants

QMRCenturiation (in Latin centuriatio or, more usually, limitatio[1]) was a method of land measurement used by the Romans. In many cases land divisions based on the survey formed a field system, often referred to in modern times by the same name. According to O. A. W. Dilke,[2] centuriation combined and developed features of land surveying present in Egypt, Etruria, Greek towns and Greek countryside.

Centuriation is characterised by the regular layout of a square grid traced using surveyors' instruments. It may appear in the form of roads, canals and agricultural plots. In some cases these plots, when formed, were allocated to Roman army veterans in a new colony, but they might also be returned to the indigenous inhabitants, as at Orange (France).[3]

The study of centuriation is very important for reconstructing landscape history in many former areas of the Roman empire.

The Romans constructed their cities with quadrant grids

It has been suggested that the Roman centuriation system inspired Thomas Jefferson's proposal to create a grid of townships for survey purposes, which ultimately led to the United States Public Land Survey System. The similarity of the two systems is empirically obvious in certain parts of Italy, for example, where traces of centuriation have remained.[8]

However, Thrower points out that, unlike the later US system, "not all Roman centuriation displays consistent orientation".[9]

This is because, for practical reasons, the orientation of the axes did not always coincide with the four cardinal points and followed instead the orographic features of the area, also taking into account the slope of the land and the flow of rainwater along the drainage channels that were traced (centuriation of Florentia (Florence). In other cases, it was based on the orientation of existing lines of communication (centuriation along the Via Emilia) or other geomorphological features.

Centuriation is typical of flat land, but centuriation systems have also been documented in hilly country.

QMrA simple grid plan road map (Windermere, Florida).

QMRSurveyor's plan of Salt Lake City, circa 1870s - an example of a typical, uniform, square-grid street network

QMRStraight road in the Province of Bergamo, Italy, following line of Roman Grid

QMRBarcelona is composed of quadrant grids

QMROuagadougou, 1930 is made up of a quadrant grid layout

QMR Commissioners' Plan of 1811 for Manhattan was a quadrant grid layout

QMRgridiron

Contents [hide]

1 English

1.1 Etymology

1.2 Pronunciation

1.3 Noun

1.3.1 Synonyms

1.3.2 Related terms

1.3.3 Translations

1.3.4 See also

English[edit]

Wikipedia has an article on:

gridiron

Etymology[edit]

Origin uncertain; the ending was assimilated to iron.

A gridiron

Pronunciation[edit]

(UK) IPA(key): /ˈɡɹɪdaɪən/

Noun[edit]

gridiron (plural gridirons)

An instrument of torture on which people were secured before being burned by fire. [from 13th c.] [quotations ▼]

An iron rack or grate used for broiling flesh and fish over coals. [from 14th c.]

Any object resembling the rack or grate. [from 15th c.]

(nautical) An openwork frame on which vessels are placed for examination, cleaning, and repairs.

(American football) The field on which American football is played. [from 19th c.]

(uncountable) American football. [quotations ▼]

(Australia and New Zealand) A generic term for American and Canadian football, particularly when used to distinguish from other codes of football.

Synonyms[edit]

football field

Painting chapter

QMRChex is a brand of breakfast cereal, introduced in 1937 and currently manufactured by General Mills. It was originally owned by St. Louis, Missouri-based Ralston Purina, and the Chex name reflects the "checkerboard square" logo of Ralston Purina.[citation needed] The product line was part of the spinoff of the Ralston portion of Ralston Purina into Ralcorp in 1994. The product line was sold to General Mills in 1997. For many years, advertisements for the cereal featured the characters from Charles M. Schulz's Peanuts comic strip.

An old box of Corn Chex.

It gains its name from the checkered pattern on the woven grain mixes of the various cereals.

QMRFantasy Creatures (and everything else) are made out of four basic forms– cube, sphere, cone, and cylinder. If you can draw and shade these forms well, it will help you greatly to create, draw, and shade whatever fantasy creature you imagine.

These are the four basic forms of graphic design

QMRThe WSB-TV tower is a 327.6 metres (1,075 ft) guyed mast broadcast tower in the Old Fourth Ward neighborhood of Atlanta, Georgia, immediately adjacent to Freedom Parkway and the Historic Fourth Ward Park skatepark.

WSB TV Tower was built in 1957 and at its completion was the tallest guyed mast tower in the United States. It has a triangular cross section.

This tower is so close to Freedom Parkway that one of its three sets of guy-wires goes over the road. To prevent falling ice in winter, the roadway is covered.[1]

FM TV

It is comprised of lattice quadrants

QMRLatticework is an openwork framework consisting of a criss-crossed pattern of strips of building material, typically wood or metal. The design is created by crossing the strips to form a network.[1] Latticework can be purely ornamental, or can be used as a truss structure such as a lattice girder bridge.[2]

In India, the house of a rich or noble person may be built with a baramdah or verandah surrounding every level leading to the living area. The upper floors often have balconies overlooking the street that are shielded by jalis (latticed screens) carved in stone latticework that keeps the area cool and gives privacy.[3]

Latticework is popular in fences . Lattices look like quadrants.

QMRA jali or jaali, (Hindi:जाली jālī, meaning "net") is the term for a perforated stone or latticed screen, usually with an ornamental pattern constructed through the use of calligraphy and geometry. This form of architectural decoration is found in Indian architecture, Indo-Islamic Architecture and Islamic Architecture.[1]

Early jali work was built by carving into stone, generally in geometric patterns, while later the Mughals used very finely carved plant-based designs, as at the Taj Mahal. They also often added pietra dura inlay to the surrounds, using marble and semi-precious stones.[2][3]

QMRA lattice girder is a girder where the flanges are connected by a lattice web.[

The lattice girder type of design has been supplanted in modern construction with welded or bolted plate girders, which use more material but have lower fabrication and maintenance costs. The lattice girder was used prior to the development of larger rolled steel plates.

The term is also sometimes used to refer to a structural member commonly made using a combination of structural sections connected with diagonal lacing. This member is more correctly referred to as a laced strut[2] or laced tie, as it normally resists axial compression (strut) or axial tension (tie); the lattice girder, like any girder, primarily resists bending.

The component sections may typically include metal beams, channel and angle sections, with the lacing elements either metal plate strips, or angle sections. The lacing elements are typically attached using either hot rivets or threaded locator bolts. As with lattice girders, laced struts and ties have generally been supplanted by hollow box sections, which are more economic with modern technology. In some case seismic retrofit modifications replace riveted lacing with plates bolted in place.

This example shows laced struts and ties. Pure tension eyebars are seen in the background (this is the cantilever portion of the old abandoned eastern span of the San Francisco – Oakland Bay Bridge).

They are quadrants

QMRSome structures employing lattice girders[edit]

Manhattan Bridge.

Runcorn Railway Bridge.

Kew Railway Bridge.

Dowery Dell Viaduct, demolished 1964.

Bennerley Viaduct.

Some structures employing laced struts or ties[edit]

The Eiffel Tower.

The obsolescent eastern span of the San Francisco–Oakland Bay Bridge. The western span has been retrofitted with bolted plates replacing the lacing for added strength.The eastern span has been replaced.

The internal structure of the Statue of Liberty.

The sides of the Cape Fear Memorial Bridge.

See also[edit]

Lattice truss bridge — an extension of the concept to form a deep truss

Hares Hill Road Bridge

QMR The Eiffel Tower (/ˈaɪfəl ˈtaʊər/ eye-fəl towr; French: tour Eiffel [tuʁ‿ɛfɛl] About this sound listen) is a wrought iron lattice tower on the Champ de Mars in Paris, France. It is named after the engineer Gustave Eiffel, whose company designed and built the tower. Constructed in 1889 as the entrance to the 1889 World's Fair, it was initially criticized by some of France's leading artists and intellectuals for its design, but has become a global cultural icon of France and one of the most recognisable structures in the world.[1] The tower is the tallest structure in Paris and the most-visited paid monument in the world: 6.98 million people ascended it in 2011.[2] The tower received its 250 millionth visitor in 2010.[2]

It is composed of lattices/quadrants

The design of the Eiffel Tower was the product of Maurice Koechlin and Émile Nouguier, two senior engineers working for the Compagnie des Établissements Eiffel, after discussion about a suitable centrepiece for the proposed 1889 Exposition Universelle, a world's fair that would celebrate the centennial of the French Revolution. In May 1884, working at home, Koechlin made a sketch of their idea, described by him as "a great pylon, consisting of four lattice girders standing apart at the base and coming together at the top, joined together by metal trusses at regular intervals".[3] Eiffel initially showed little enthusiasm, but he did approve further study, and the two engineers then asked Stephen Sauvestre, the head of company's architectural department, to contribute to the design. Sauvestre added decorative arches to the base of the tower, a glass pavilion to the first level, and other embellishments.

The new version gained Eiffel's support: he bought the rights to the patent on the design which Koechlin, Nougier, and Sauvestre had taken out, and the design was exhibited at the Exhibition of Decorative Arts in the autumn of 1884 under the company name. On 30 March 1885, Eiffel presented his plans to the Société des Ingénieurs Civils; after discussing the technical problems and emphasising the practical uses of the tower, he finished his talk by saying the tower would symbolise, [4]

"Not only the art of the modern engineer, but also the century of Industry and Science in which we are living, and for which the way was prepared by the great scientific movement of the eighteenth century and by the Revolution of 1789, to which this monument will be built as an expression of France's gratitude."Aesthetics

The tower was originally painted in three shades: lighter at the top, getting progressively darker towards the bottom to perfectly complement the Parisian sky.[56] The colour is periodically changed; as of 2013 the tower is bronze coloured.[57] On the first level are interactive consoles hosting a poll for the colour to use for the next repaint.

The only non-structural elements are the four decorative grill-work arches, added in Sauvestre's sketches, which served to make the tower look more substantial and to make a more impressive entrance to the exposition.[58]

One of the great Hollywood movie clichés is that the view from a Parisian window always includes the tower. In reality, since zoning restrictions limit the height of most buildings in Paris to seven storeys, only a small number of tall buildings have a clear view of the tower.

The Eiffel Towers four legs make it reminiscent of a quadrant

QMRTaller structures

Although it was the world's tallest structure when completed in 1889, the Eiffel Tower has since lost its standing both as the tallest lattice tower and as the tallest structure in France.

Lattice towers taller than the Eiffel Tower

Further information: List of tallest towers in the world and Observation deck

Name Pinnacle height Year Country Town Remarks

Tokyo Skytree 2,080 ft (634 m) 2011 Japan Tokyo

Kiev TV Tower 1,263 ft (385 m) 1973 Ukraine Kiev

Tashkent Tower 1,230 ft (375 m) 1985 Uzbekistan Tashkent

Pylons of Zhoushan Island Overhead Powerline Tie 1,214 ft (370 m) 2009 China Jiangyin Two towers; tallest electricity pylons in the world

Pylons of Yangtze River Crossing 1,137 ft (347 m) 2003 China Jiangyin Two towers

Dragon Tower 1,102 ft (336 m) 2000 China Harbin

Tokyo Tower 1,091 ft (333 m) 1958 Japan Tokyo

WITI TV Tower 1,078 ft (329 m) 1962 U.S. Shorewood, Wisconsin

WSB TV Tower 1,075 ft (328 m) 1957 U.S. Atlanta, Georgia

Caricature of Gustave Eiffel comparing the Eiffel tower to the Pyramids

QMRLattice pastry is a pastry used in a criss-crossing pattern of strips in the preparation of various foods. Latticed pastry is used as a type of lid on many various tarts and pies. The openings between the lattice allows fruit juices in pie fillings to evaporate during the cooking process, which can caramelize the filling.[1]

QMRA croline is a flaky (typically puff) pastry[1] parcel filled with various (traditionally) salty or spicy fillings. Normally the top side of the pastry is latticed. Crolines are produced in various shapes and sizes and with different fillings. Though sweet versions are beginning to be produced, typical savoury fillings are mushroom, ham/cheese and salmon/herb. (Seafood filled crolines are normally made in a fish shaped pastry.)

waffles tend to have a quadrant pattern engrained in them

QMRTokyo Skytree (東京スカイツリー Tōkyō Sukaitsurī?) is a broadcasting, restaurant, and observation tower in Sumida, Tokyo, Japan. It became the tallest structure in Japan in 2010[2] and reached its full height of 634.0 metres (2,080 ft) in March 2011, making it the tallest tower in the world, displacing the Canton Tower,[3][4] and the second tallest structure in the world after the Burj Khalifa (829.8 m/2,722 ft).[5]

It has a lattice structure design

QMRThe Kiev TV Tower (Ukrainian: Телевізійна вежа, Televiziyna vezha) is a 385 m-high (1,263 ft) lattice steel tower built in 1973 in Kiev, Ukraine, for radio and television broadcasting. It is the tallest freestanding lattice steel construction in the world.[1][dubious – discuss] The tower in Oranzhereina Street is not open to the public.

It has a lattice quadrant structure

QMRA lattice graph, mesh graph, or grid graph, is a graph whose drawing, embedded in some Euclidean space Rn, forms a regular tiling. This implies that the group of bijective transformations that send the graph to itself is a lattice in the group-theoretical sense.

Typically, no clear distinction is made between such a graph in the more abstract sense of graph theory, and its drawing in space (often the plane or 3D space). This type of graph may more shortly be called just a lattice, mesh, or grid. Moreover, these terms are also commonly used for a finite section of the infinite graph, as in "an 8×8 square grid".

The term lattice graph has also been given in the literature to various other kinds of graphs with some regular structure, such as the Cartesian product of a number of complete graphs.[1]

QMRSquare grid graph[edit]

A common type of a lattice graph (known under different names, such as square grid graph) is the graph whose vertices correspond to the points in the plane with integer coordinates, x-coordinates being in the range 1,..., n, y-coordinates being in the range 1,..., m, and two vertices are connected by an edge whenever the corresponding points are at distance 1. In other words, it is a unit distance graph for the described point set.[2]

Properties[edit]

A square grid graph is a Cartesian product of graphs, namely, of two path graphs with n - 1 and m - 1 edges.[2] Since a path graph is a median graph, the latter fact implies that the square grid graph is also a median graph. All grid graphs are bipartite, which is easily verified by the fact that one can color the vertices in a checkerboard fashion.

A path graph may also be considered to be a grid graph on the grid n times 1. A 2x2 grid graph is a 4-cycle.[2]

Other kinds[edit]

A triangular grid graph is a graph that corresponds to a triangular grid.

A Hanan grid graph for a finite set of points in the plane is produced by the grid obtained by intersections of all vertical and horizontal lines through each point of the set.

The rook's graph (the graph that represents all legal moves of the rook chess piece on a chessboard) is also sometimes called the lattice graph.

QMRThe Tashkent Television Tower (Uzbek: Toshkent Teleminorasi) is a 365 metres (1,198 ft) high tower, located in Tashkent, Uzbekistan. Construction started in 1978 and it began operation 6 years later, on 15 January 1985. It was the 3rd tallest tower in the world from 1985 to 1991.

It is of a vertical cantilever structure, and is constructed out of steel. Its architectural design is a product of the Terxiev, Tsarucov & Semashko firm.

The tower has an observation deck located 97 metres (318 ft) above the ground. It is the tallest structure in Central Asia. It also belongs to the World Federation of Great Towers, ranking as the 8th tallest.

Use[edit]

The main purposes of the tower are radio and TV-transmission. The signal reaches the farthest points of Tashkent Province and some of the south regions of Kazakhstan. The tower is also used for communication between governmental departments, and organizations. The tower also serves as a complex hydrometeorological station.

It is comprised of lattice quadrants

QMRThe Zhoushan Island Overhead Powerline Tie is a 220 kV three-phase AC interconnection of the power grid of Zhoushan Island with that of the Chinese mainland. It runs over several islands and consists of several long distance spans, the longest with a length of 2.7 kilometres (1.7 mi) south of Damao Island. This span uses two 370-metre-tall (1,210 ft) pylons, which are the tallest electricity pylons in the world. The north tower on Damao Island (Chinese: 大猫岛, dà māo dǎo) was completed in 2009, and the south tower on Liangmao Island (Chinese: 凉帽岛, liángmào dǎo) was completed in 2010. These pylons resemble those of the Messina Strait, but are steel-tube lattice structures. It is made of lattice quadrants

QMRLattice path

From Wikipedia, the free encyclopedia

Lattice path of length 5 in \mathbb {Z} ^{2} with S=\left\{(2,0),(1,1),(0,-1)\right\}.

In combinatorics, a lattice path L in \mathbb {Z} ^{d} of length k with steps in S is a sequence v_{0},v_{1},\ldots ,v_{k}\in \mathbb {Z} ^{d} such that each consecutive difference v_{i}-v_{i-1} lies in S. [1] A lattice path may lie in any lattice in \mathbb {R} ^{d},[1] but the integer lattice \mathbb {Z} ^{d} is most commonly used.

An example of a lattice path in \mathbb {Z} ^{2} of length 5 with steps in S=\lbrace (2,0),(1,1),(0,-1)\rbrace is L=\lbrace (-1,-2),(0,-1),(2,-1),(2,-2),(2,-3),(4,-3)\rbrace .

Contents [hide]

1 North-East lattice paths

2 Counting lattice paths

3 Combinations and NE lattice paths

3.1 Problems and proofs

4 References

North-East lattice paths[edit]

A North-East (NE) lattice path is a lattice path in \mathbb {Z} ^{2} with steps in S=\lbrace (0,1),(1,0)\rbrace . The (0,1) steps are called North steps and denoted by N's; the (1,0) steps are called East steps and denoted by E's.

NE lattice paths most commonly begin at the origin. This convention allows us to encode all the information about a NE lattice path L in a single permutation word. The length of the word gives us the number of steps of the lattice path, k. The order of the N's and E's communicates the sequence of L. Furthermore, the number of N's and the number of E's in the word determines the end point of L.

If the permutation word for a NE lattice path contains n Nsteps and e E steps, and if the path begins at the origin, then the path necessarily ends at (e,n). This follows because you have "walked" exactly n steps North and e steps East from (0,0).

Lattice paths are on quadrant grids

Counting lattice paths[edit]

Lattice paths are often used to count other combinatorial objects. Similarly, there are many combinatorial objects that count the number of lattice paths of a certain kind. This occurs when the lattice paths are in bijection with the object in question. For example,

Dyck paths are counted by the n^{\text{th}} Catalan number C_{n}. A Dyck path is a lattice path in \mathbb {Z} ^{2} from (0,0) to (2n,0) with steps in S=\lbrace (1,1),(1,-1)\rbrace that never passes below the x-axis.[2] Equivalently, a Dyck path is a NE lattice path from (0,0) to (n,n) that lies strictly below (but may touch) the diagonal y=x.[2][3]

The Schröder numbers count the number of lattice paths from (0,0) to (n,n) with steps in (1,0),(0,1) and (1,1) that never rise above the diagonal y=x.[2]

The number of NE lattice paths from (0,0) to (a,b) counts the number of combinations of a objects out of a set of a+b objects.

Combinations and NE lattice paths[edit]

NE lattice paths have close connections to the number of combinations, which are counted by the binomial coefficient, and arranged in Pascal's triangle. The diagram below demonstrates some of these connections.

The number of lattice paths from (0,0) to (2,3) is equal to {\binom {2+3}{2}}={\binom {5}{2}}=10.

The number of lattice paths from (0,0) to (n,k) is equal to the binomial coefficient {\binom {n+k}{n}}. The diagram shows this for 0\leq k\leq n=4. If one rotates the diagram 135° clockwise about the origin and extend it to include all n,k\in \mathbb {N} \cup \lbrace 0\rbrace , one obtains Pascal's triangle. This result is no surprise, because the k^{\text{th}} entry of the n^{\text{th}} row of Pascal's Triangle is the binomial coefficient {\binom {n}{k}}.

QMRTextiles can be made from many materials. These materials come from four main sources: animal (wool, silk), plant (cotton, flax, jute), mineral (asbestos, glass fibre), and synthetic (nylon, polyester, acrylic). In the past, all textiles were made from natural fibres, including plant, animal, and mineral sources. In the 20th century, these were supplemented by artificial fibres made from petroleum.

Textiles are made in various strengths and degrees of durability, from the finest gossamer to the sturdiest canvas. Microfibre refers to fibres made of strands thinner than one denier.

Animal textiles[edit]

Animal textiles are commonly made from hair, fur, skin or silk (in the silkworms case).

Wool refers to the hair of the domestic goat or sheep, which is distinguished from other types of animal hair in that the individual strands are coated with scales and tightly crimped, and the wool as a whole is coated with a wax mixture known as lanolin (sometimes called wool grease), which is waterproof and dirtproof[citation needed]. Woollen refers to a bulkier yarn produced from carded, non-parallel fibre, while worsted refers to a finer yarn spun from longer fibres which have been combed to be parallel. Wool is commonly used for warm clothing. Cashmere, the hair of the Indian cashmere goat, and mohair, the hair of the North African angora goat, are types of wool known for their softness.

Other animal textiles which are made from hair or fur are alpaca wool, vicuña wool, llama wool, and camel hair, generally used in the production of coats, jackets, ponchos, blankets, and other warm coverings. Angora refers to the long, thick, soft hair of the angora rabbit. Qiviut is the fine inner wool of the muskox.

Wadmal is a coarse cloth made of wool, produced in Scandinavia, mostly 1000~1500 CE.

Silk is an animal textile made from the fibres of the cocoon of the Chinese silkworm which is spun into a smooth fabric prized for its softness. There are two main types of the silk: 'mulberry silk' produced by the Bombyx Mori, and 'wild silk' such as Tussah silk. Silkworm larvae produce the first type if cultivated in habitats with fresh mulberry leaves for consumption, while Tussah silk is produced by silkworms feeding purely on oak leaves. Around four-fifths of the world's silk production consists of cultivated silk.[11]

Plant textiles[edit]

Grass, rush, hemp, and sisal are all used in making rope. In the first two, the entire plant is used for this purpose, while in the last two, only fibres from the plant are utilized. Coir (coconut fibre) is used in making twine, and also in floormats, doormats, brushes, mattresses, floor tiles, and sacking.

Traditional textile making tools from 14th century Persia

Straw and bamboo are both used to make hats. Straw, a dried form of grass, is also used for stuffing, as is kapok.

Fibres from pulpwood trees, cotton, rice, hemp, and nettle are used in making paper.

Cotton, flax, jute, hemp, modal and even bamboo fibre are all used in clothing. Piña (pineapple fibre) and ramie are also fibres used in clothing, generally with a blend of other fibres such as cotton. Nettles have also been used to make a fibre and fabric very similar to hemp or flax. The use of milkweed stalk fibre has also been reported, but it tends to be somewhat weaker than other fibres like hemp or flax.

The inner bark of the lacebark tree is a fine netting that has been used to make clothing and accessories as well as utilitarian articles such as rope.

Acetate is used to increase the shininess of certain fabrics such as silks, velvets, and taffetas.

Seaweed is used in the production of textiles: a water-soluble fibre known as alginate is produced and is used as a holding fibre; when the cloth is finished, the alginate is dissolved, leaving an open area.

Lyocell is a synthetic fabric derived from wood pulp. It is often described as a synthetic silk equivalent; it is a tough fabric that is often blended with other fabrics – cotton, for example.

Fibres from the stalks of plants, such as hemp, flax, and nettles, are also known as 'bast' fibres.

Mineral textiles[edit]

Asbestos and basalt fibre are used for vinyl tiles, sheeting, and adhesives, "transite" panels and siding, acoustical ceilings, stage curtains, and fire blankets.

Glass fibre is used in the production of ironing board and mattress covers, ropes and cables, reinforcement fibre for composite materials, insect netting, flame-retardant and protective fabric, soundproof, fireproof, and insulating fibres. Glass fibres are woven and coated with Teflon to produce beta cloth, a virtually fireproof fabric which replaced nylon in the outer layer of United States space suits since 1968.

Metal fibre, metal foil, and metal wire have a variety of uses, including the production of cloth-of-gold and jewellery. Hardware cloth (US term only) is a coarse woven mesh of steel wire, used in construction. It is much like standard window screening, but heavier and with a more open weave. It is sometimes used together with screening on the lower part of screen doors, to resist scratching by dogs. It serves similar purposes as chicken wire, such as fences for poultry and traps for animal control.

Synthetic textiles[edit]

A variety of contemporary fabrics. From the left: evenweave cotton, velvet, printed cotton, calico, felt, satin, silk, hessian, polycotton.

Woven tartan of Clan Campbell, Scotland.

Embroidered skirts by the Alfaro-Nùñez family of Cochas, Peru, using traditional Peruvian embroidery methods.[12]

All synthetic textiles are used primarily in the production of clothing.

Polyester fibre is used in all types of clothing, either alone or blended with fibres such as cotton.

Aramid fibre (e.g. Twaron) is used for flame-retardant clothing, cut-protection, and armor.

Acrylic is a fibre used to imitate wools, including cashmere, and is often used in replacement of them.

Nylon is a fibre used to imitate silk; it is used in the production of pantyhose. Thicker nylon fibres are used in rope and outdoor clothing.

Spandex (trade name Lycra) is a polyurethane product that can be made tight-fitting without impeding movement. It is used to make activewear, bras, and swimsuits.

Olefin fibre is a fibre used in activewear, linings, and warm clothing. Olefins are hydrophobic, allowing them to dry quickly. A sintered felt of olefin fibres is sold under the trade name Tyvek.

Ingeo is a polylactide fibre blended with other fibres such as cotton and used in clothing. It is more hydrophilic than most other synthetics, allowing it to wick away perspiration.

Lurex is a metallic fibre used in clothing embellishment.

Milk proteins have also been used to create synthetic fabric. Milk or casein fibre cloth was developed during World War I in Germany, and further developed in Italy and America during the 1930s.[13] Milk fibre fabric is not very durable and wrinkles easily, but has a pH similar to human skin and possesses anti-bacterial properties. It is marketed as a biodegradable, renewable synthetic fibre.[14]

Carbon fibre is mostly used in composite materials, together with resin, such as carbon fibre reinforced plastic. The fibres are made from polymer fibres through carbonization.

QMR Mosaics are made up of square pieces like quadrants

Mosaic is the art of creating images with an assemblage of small pieces of colored glass, stone, or other materials. It is a technique of decorative art or interior decoration. Most mosaics are made of small, flat, roughly square, pieces of stone or glass of different colors, known as tesserae; but some, especially floor mosaics, may also be made of small rounded pieces of stone, and called "pebble mosaics".

Mosaic has a long history, starting in Mesopotamia in the 3rd millennium BC. Pebble mosaics were made in Tiryns in Mycenean Greece; mosaics with patterns and pictures became widespread in classical times, both in Ancient Greece and Ancient Rome. Early Christian basilicas from the 4th century onwards were decorated with wall and ceiling mosaics. Mosaic art flourished in the Byzantine Empire from the 6th to the 15th centuries; that tradition was adopted by the Norman kingdom in Sicily in the 12th century, by eastern-influenced Venice, and among the Rus in Ukraine. Mosaic fell out of fashion in the Renaissance, though artists like Raphael continued to practise the old technique. Roman and Byzantine influence led Jews to decorate 5th and 6th century synagogues in the Middle East with floor mosaics.

Mosaic was widely used on religious buildings and palaces in early Islamic art, including Islam's first great religious building, the Dome of the Rock in Jerusalem, and the Umayyad Mosque in Damascus. Mosaic went out of fashion in the Islamic world after the 8th century.

Modern mosaics are made by professional artists, street artists, and as a popular craft. Many materials other than traditional stone and ceramic tesserae may be employed, including shells, glass and beads.

QMRPiqué, or marcella, refers to a weaving style, normally used with cotton yarn, which is characterized by raised parallel cords or fine ribbing. Twilled cotton and corded cotton are close relatives.

The weave is closely associated with white tie, and some accounts even say the fabric was invented specifically for this use. It holds more starch than plain fabric, so produces a stiffer shirt front. Marcella shirts then replaced earlier plain fronts, which remain a valid alternative. Marcella's use then spread to other parts of the dress code and it is now the most common fabric used in the tie and waistcoat of white tie. A knit fabric with a similar texture is used in polo shirts.

Marcella weaving was developed by the Lancashire cotton industry in the late 18th century as a mechanised technique of weaving double cloth with an enclosed heavy cording weft.[1] It was originally used to make imitations of the corded Provençal quilts made in Marseille, the manufacture of which became an important industry for Lancashire from the late 18th to the early 20th century.[1] The term "marcella" is one of a number of variations on the word "Marseille".[2]

Pique fabrics are a type of dobby construction. Piques may be constructed in various patterns such as cord, waffle, honeycomb and birdseye piques. These fabrics require the addition of extra yarns, called stuffer yarns. These stuffer yarns are incorporated into the back of the fabric to give texture and added depth to the fabric design. Some piques may be made using the Jacquard attachment on the loom. Although made of 100% cotton today, cotton-silk blends and even pure silk versions were made in the past and in a variety of weaves. If you look closely at a pique weave it is comprised of quadrants

QMRPlain weave

From Wikipedia, the free encyclopedia

An example of the thread crossing pattern in a plain weave fabric.

Structure of plain-woven fabric

Structure of basketweave fabric

Plain weave (also called tabby weave, linen weave[1] or taffeta weave) is the most basic of three fundamental types of textile weaves (along with satin weave and twill).[2] It is strong and hard-wearing, used for fashion and furnishing fabrics.

In plain weave, the warp and weft are aligned so they form a simple criss-cross pattern. Each weft thread crosses the warp threads by going over one, then under the next, and so on. The next weft thread goes under the warp threads that its neighbor went over, and vice versa.

Balanced plain weaves are fabrics in which the warp and weft are made of threads of the same weight (size) and the same number of ends per inch as picks per inch.[3]

Basketweave is a variation of plain weave in which two or more threads are bundled and then woven as one in the warp or weft, or both.

A balanced plain weave can be identified by its checkerboard-like appearance. It is also known as one-up-one-down weave or over and under pattern.[4]

Some examples of fabric with plain weave are chiffon, organza, and taffeta.

Plain weave is made up of quadrants

QMRChiffon uses plain weave, which is a quadrant weave. Chiffon (French pronunciation: [ʃi.fɔ̃]; English pronunciation /ʃɪˈfɒn/, shiff-on, from the French word for a cloth or rag) is a lightweight, balanced plain-woven sheer fabric woven of alternate S- and Z-twist crepe (high-twist) yarns.[1] The twist in the crepe yarns puckers the fabric slightly in both directions after weaving, giving it some stretch and a slightly rough feel.

Chiffon is made from cotton, silk, or synthetic fibers. Under a magnifying glass it resembles a fine net or mesh which gives chiffon some see-through properties. Chiffon made from natural fibers can be dyed to almost any shade, but chiffon made from polyester requires specialized disperse dyes.

When sewing chiffon, many crafters layer tissue paper in between the two pieces being sewn together. The tissue paper helps keep the fabric together, with the rough surface of the tissue holding the chiffon in place while it is handled. After sewing, the tissue paper can be carefully ripped out. Chiffon is also pinnable, as it will spring back, concealing pin marks. As a general rule, sewers are advised to work slowly and steadily with this fabric, taking care not to run it through a sewing machine too quickly lest it bunch and gather.

Chiffon is most commonly used in evening wear, especially as an overlay, for giving an elegant and floating appearance to the gown. It is also a popular fabric used in blouses, ribbons, scarves and lingerie. Like other crêpe fabrics, chiffon can be difficult to work with because of its light and slippery texture. Due to this delicate nature, chiffon must be hand washed very gently.[1]

Since chiffon is a light-weight fabric that frays very easily, bound or French seams must be used to stop the fabric from fraying. Chiffon is smoother and more lustrous than the similar fabric georgette. Chiffon is also known as a very light pink.

QMRTaffeta (/ˈtæfɨtə/; archaically spelled taffety) is a crisp, smooth, plain woven fabric made from silk or cuprammonium rayons. The word is Persian in origin and means "twisted woven." It is considered to be a "high-end" fabric, suitable for use in ball gowns, wedding dresses, and interiors for curtains or wallcovering. It is also widely used in the manufacture of corsets and corsetry: it yields a more starched-like type of cloth that holds its shape better than many other fabrics. An extremely thin, crisp type of taffeta is called paper taffeta.[1][2]

There are two distinct types of silk taffeta: yarn-dyed and piece-dyed. Piece-dyed taffeta is often used in linings and is quite soft. Yarn-dyed taffeta is much stiffer and is often used in evening dresses. Shot silk taffeta was one of the most sought-after forms of Byzantine silk, and may have been the fabric known as purpura.[3]

Production[edit]

Modern taffeta was first woven in Italy and France and until the 1950s in Japan. Warp-printed taffeta or chiné, mainly made in France from the eighteenth century onwards, is sometimes called "pompadour taffeta" after Madame de Pompadour.[4] Today most raw silk taffeta is produced in India and Pakistan. Initially, handlooms were widely used, but since the 1990s it has been produced on mechanical looms in the Bangalore area. From the 1970s until the 1990s, the Jiangsu province of China produced fine silk taffetas: these were less flexible than those from Indian mills, however, which continue to dominate production. Other countries in Southeast Asia and the Middle East also produce silk taffeta, but these products are not yet equal in quality or competitiveness to those from India. The most deluxe taffetas, however, are still woven in France, Italy, Russia, and the United Kingdom.[citation needed]

Historical and current uses[edit]

Taffeta has seen use for purposes other than clothing fabric, including the following:

On November 4, 1782, taffeta was used by Joseph Montgolfier of France to construct a small, cube-shaped balloon. This was the beginning of many experiments using taffeta balloons by the Montgolfier brothers, and led to the first known human flight in a lighter-than-air craft.[citation needed]

Synthetic fibre forms of taffeta have been used to simulate the structure of blood vessels.[5]

QMRSatin (/ˈsætən/[1]) is a weave that typically has a glossy surface and a dull back. The satin weave is characterized by four or more fill or weft yarns floating over a warp yarn or vice versa, four warp yarns floating over a single weft yarn. Floats are missed interfacings, where the warp yarn lies on top of the weft in a warp-faced satin and where the weft yarn lies on top of the warp yarns in weft-faced satins. These floats explain the even sheen, as unlike in other weaves, the light reflecting is not scattered as much by the fibres, which have fewer tucks. Satin is usually a warp-faced weaving technique in which warp yarns are "floated" over weft yarns, although there are also weft-faced satins.[2] If a fabric is formed with a satin weave using filament fibres such as silk, nylon, or polyester, the corresponding fabric is termed a satin, although some definitions insist that the fabric be made from silk.[3] If the yarns used are short-staple yarns such as cotton, the fabric formed is considered a sateen.

A satin fabric tends to have a high luster due to the high number of floats on the fabric. Because of this it is used in making bed sheets. Many variations can be made of the basic satin weave including a granite weave and a check weave. Satin weaves, twill weaves, and plain weaves are the three basic types of weaving by which the majority of woven products are formed.

Satin is commonly used in apparel: satin baseball jackets, athletic shorts, women's lingerie, nightgowns, blouses, and evening gowns, but also in some men's boxer shorts, briefs, shirts and neckties. It is also used in the production of pointe shoes for use in ballet. Other uses include interior furnishing fabrics, upholstery, and bed sheets.

With the warp and weft the satin weaving also has a sort of quadrant reflection

QMRDiamond twill, with weaving edge (left), blue warp, red weft- looks like quadrants

QMRTwill is a type of textile weave with a pattern of diagonal parallel ribs (in contrast with a satin and plain weave). This is done by passing the weft thread over one or more warp threads and then under two or more warp threads and so on, with a "step" or offset between rows to create the characteristic diagonal pattern.[1] Because of this structure, twill generally drapes well.

Twill with the orthogonal warp and weft still resembles quadrants

Classification[edit]

Twill weaves can be classified from four points of view:

According to the way of construction

Warp-way: 3/1 warp way twill, etc.

Weft-way: 2/3 weft way twill, etc.

According to the direction of twill lines on the face of the fabric

S – Twill or left-hand twill weave: 2/1 S, etc.

Z – Twill or right hand twill weave: 3/2 Z, etc.

According to the face yarn (warp or weft)

Warp face twill weave: 4/2 S, etc.

Weft face twill weave: 1/3 Z, etc.

Double face twill weave: 3/3 Z, etc.

According to the nature of the produced twill line

Simple twill weave: ½ S, 3/1 Z etc.

Expanded twill weave: 4/3 S, 3/2 Z, etc.

Multiple twill weave: (2 3)/(3 1) S, etc.

QMRCertainly the most famous of the La Venta monumental artifacts are the four colossal heads. Seventeen colossal heads have been unearthed in the Olmec area, four of them at La Venta, officially named Monuments 1 through 4.

Three of the heads—Monuments 2, 3, & 4—were found roughly 150 meters north of Complex A, which is itself just north of the Great Pyramid. These heads were in a slightly irregular row, facing north. The other colossal head—Monument 1 (shown at left) – is a few dozen meters south of the Great Pyramid. The fourth is always different from the first three

The La Venta heads are thought to have been carved by 700 BCE, but possibly as early as 850 BCE, while the San Lorenzo heads are credited to an earlier period. The colossal heads can measure up to 9 feet 4 inches (2.84 m) in height and weigh several tons. The sheer size of the stones causes a great deal of speculation on how the Olmec were able to move them. The major basalt quarry for the colossal heads at La Venta was found at Cerro Cintepec in the Tuxtla Mountains, over 80 km away.[21]

Each of the heads wears headgear reminiscent of 1920s-style American football helmets, although each is unique in its decoration. The consensus is that the heads likely represent mighty Olmec rulers.

QMRAlso unearthed in Complex A were three rectangular mosaics (also known as "Pavements") each roughly 4.5 by 6 metres (15 by 20 feet) and each consisting of up to 485 blocks of serpentine. These blocks were arranged horizontally to form what has been variously interpreted as an ornate Olmec bar-and-four-dots motif, the Olmec Dragon,[11] a very abstract jaguar mask,[12] a cosmogram,[13] or a symbolic map of La Venta and environs.[14] Not intended for display, soon after completion these pavements were covered over with colored clay and then many feet of earth.

Om Shri Mahalaxmi Namaha has four words

QMRCrispix (or Crispix Krispies in Canada) is a brand of breakfast cereal, introduced by Kellogg's in 1983. It was created specifically to compete with Ralston Purina's Chex family of cereals, which had about $125 million in annual sales and no significant competition. By 1987, Crispix had sales of about $65 million.[1] Honey Flavored Crispix have been sold twice in the UK, and twice have they been discontinued.

Its box touts its unique composition of "Crispy rice on one side, crunchy corn on the other."[2] The cereal itself is in a hexagon shape. The two sides are made in a lattice pattern and connected only at the edges; the center is open. Crispix is kosher/parve.[3]

Australia formerly had a honey version, and currently has a chocolate version known as Coco Pops Chex. [4]

The cereal is comprised of quadrant grids

QMRIn the 1920s, national advertising in magazines and radio broadcasts played a key role in the emergence of the fourth big cereal manufacturer, General Mills. In 1921, James Ford Bell, president of a Minneapolis wheat milling firm, began experimenting with rolled wheat flakes. After tempering, steaming, cracking wheat, and processing it with syrup, sugar, and salt, it was prepared in a pressure cooker for rolling and then dried in an electric oven. By 1925, Wheaties had become the "Breakfast of Champions". In 1928, four milling companies consolidated as the General Mills Company in Minneapolis. The new firm expanded packaged food sales with heavy advertising, including sponsorship of radio programs such as "Skippy", "Jack Armstrong, The All-American Boy", and baseball games. Jack Dempsey, Johnny Weissmuller, and others verified the "Breakfast of Champions" slogan. By 1941 Wheaties had won 12% percent of the cereal market. Experiments with the puffing process produced Kix, a puffed corn cereal, and Cheerios, a puffed oats cereal. Further product innovation and diversification brought total General Mills sales to over $500 million annually (18% in packaged foods) by the early 1950s.[24][25]

QMRQuaker Oats was founded in 1901 by the merger of four oat mills:

The Quaker Mill Company of Ravenna, Ohio, which held the trademark on the Quaker name and was founded by Henry Parsons Crowell, who bought the bankrupt Quaker Oat Mill Company, also in Ravenna.[2] He held the key positions of general manager, president and chairman of the company from 1888 until late 1943. He was called the cereal tycoon.[3] He donated more than 70% of his wealth to the Crowell Trust.[4][5][6][7][8]

A cereal mill in Cedar Rapids, Iowa owned by John Stuart, his son Robert Stuart, and their partner George Douglas;

The German Mills American Oatmeal Company, owned by "The Oatmeal King", Ferdinand Schumacher of Akron, Ohio;

The Rob Lewis & Co. American Oats and Barley Oatmeal Corporation. Formally known as "Good For Breakfast" instant oatmeal mix.

Flavours[edit]

Original Shreddies (1993–present)

Frosted Shreddies (1993–present)

Coco Shreddies (2002–present)

Honey Shreddies (2007–present)

Coco Caramel Shreddies (Caramel Shreddies outside the US) (2008–present)

Advertising[edit]

United Kingdom[edit]

For many years in the UK the Shreddies boxes featured Tom and Jerry (from the MGM cartoons). They regularly featured gifts in the boxes featuring Tom and Jerry, such as glow in the dark stickers sets, and puzzle books.

For a few years, Shreddies' advert campaigns featured a cartoon personification of "Hunger" as an antagonist. He appeared as a blue monster with big teeth whose goal it was to taunt hungry individuals by drumming on their stomachs with a pair of silver spoons. Hunger would then be dispatched when the victim consumed a bowl of Shreddies, sealing Hunger inside a shreddie cage. Despite his troublesome persona, Hunger was frequently used as a mascot for the cereal during this period.[2] The message during this time was "Shreddies keep hunger locked up 'til lunch" and most ads ended with a box of Shreddies rolling up in front of Hunger who then gets crushed in between it and a box of Frosted Shreddies zooming in from behind him.

For a while in the early 2000s, Frosted and Coco Shreddies were advertised as "too tasty for geeks." The adverts would feature "geeks" trying to eat a bowl of either Frosted or Coco Shreddies, but being overwhelmed by its taste, followed by a much cooler kid named Sure-Eddie being able to easily eat the Shreddies. In 2003, Coco Shreddies was coated with more chocolate.

In 2005, Shreddies was advertised as School fuel. The advert showed school children being focused on their work at school after eating a bowl of Shreddies for breakfast at home. This TV advert was ordered to be removed by the ASA as it was held to provide an unfair comparison between school children eating Shreddies or eating nothing, rather than a similar cereal.[3]

In 2007 Shreddies' advertising centred on the claim that they are "knitted by nanas" with shots of a factory full of grandmothers knitting Shreddies. The ad was voted the 7th favourite ad of 2007. And from 2007 - 2011 the packaging was changed to include a photo of the inner flaps of the nana who apparently knitted the specific box.

In 2010, supporting the launch of a new "Scrumptious new recipe", Shreddies launched a promotion to find new nanas, using TV, Digital and Facebook, this subsequently built a huge fan base on Facebook.[4] The fan page is now the 2nd largest cereal fansite in the world, providing entertainment, competitions and launching new ads to its loyal followers.

In 2012 the Shreddies Knitting Nanas continued to be used to represent the brand. The campaign was launched on Facebook to the fans in a 1-month build up to the premiere, with the ad going live on TV weeks later in April. The campaign message in 2012 was "Helping you through 'til lunch" (a reference to the early 90s strapline)[5][6]

A new advert in 2014 replaced the message with "Shreddies ...AND YOU'RE READY!" The advert features the song "This Is How We Do It" by Montell Jordan

Canada[edit]

In Canada the cereal has been known for many years by its musical jingle, "Good Good Whole-Wheat Shreddies". The mascots of the cereal in Canada were Freddie and Eddie, two anthropomorphic (yet legless) pieces of the cereal. Around 1993, their appearance changed to that of a younger youthful age complete with baseball caps and they also grew hair and legs. By the late 1990s, the characters were discontinued in all advertising and packaging. The cereal is now marketed as an "adult" cereal.

In January 2008, the company launched a new ad campaign for so-called "Diamond Shreddies." The tongue-in-cheek ads claimed the cereal's shape had been changed to diamond, and presented the original square Shreddies, rotated 45 degrees. Consumer reaction to the campaign has translated into a statistically significant sales increase, according to at least one media report on the campaign's success.[7] The campaign won the 2008 Grand Clio Award for Integrated (i.e. multiple media) Campaign.[8]

Collectables[edit]

In January 2012 it was reported that boxes of Shreddies dating from the early 1970s had been selling on eBay, after being discovered in a village shop. They were reported to have been selling for about £160 per box on eBay.[9]

Slogans[edit]

"Good, good wholewheat Shreddies!" (Canada)

"Eat up everyone, we'll knit more!" (UK)

"New recipe Shreddies, now tastier than ever." (UK)

"Helping you through 'till lunch!" (UK)

"Too tasty for geeks!" (UK)

"Shreddies and you're ready!" (UK)

Good news for everyone! (UK)

In Popular Culture[edit]

Shreddies featured as a plot device in the Canadian mockumentary television series created and directed by Mike Clattenburg, The Trailer Park Boys. Shreddies were part of the survival supplies Julian, Ricky and Bubbles sent with Jacob Collins and his Boys on their outing to lay a model train track across the Canada- US border in the episode We Can't Call People Without Wings Angels, So We Call Them Friends. Other supplies sent with them included liquorice and cannabis. The train track Jacob and his minions constructed was intended for use in smuggling cannabis across the Canada - US border. [10]

QMRLife (cereal)

From Wikipedia, the free encyclopedia

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Life cereal with banana slices

Life is a breakfast cereal formerly made of whole grain oats, but now also containing corn flour, whole wheat flour, and rice flour. It is distributed by the Quaker Oats Company. It was introduced in 1961.[1] The cereal's advertisements currently sport the slogan "Life is full of surprises". The Canadian product may be different, containing in 2015 20% sugar and "100% Canadian Quaker Oats."[2] This cereal, while well-known across the country, was popularized by the Goodfriend family.

It is comprised of quadrant grids

History[edit]

Life was popularized during the 1970s by an advertising campaign featuring "Mikey," a hard-to-please four-year-old-boy portrayed by John Gilchrist. His two older brothers were portrayed by his real-life brothers, Michael and Tommy.[3] The commercials featured the catchphrase "He likes it! Hey Mikey!" The ad campaign ran from 1972 to 1986,[4] becoming one of the longest-running television advertisements. As recently as 1999 the commercial was included in a list of "memorable ads".[5] A subsequent commercial repeated the identical dialog and scenario, using lumberjacks instead of children.

Earlier when Life cereal was first introduced, the original slogan was "The most useful protein ever in a ready to eat cereal". The original mascots (in commercials, narrated by Paul Frees) were little munchkin-like characters.

Varieties[edit]

In 1978, Cinnamon Life was introduced, followed shortly thereafter by Raisin Life. Today Cinnamon Life accounts for a third of total Life sales. Raisin Life wasn't as popular and was discontinued sometime in the mid 1980s. In 2002,[6] a short-lived version called Baked Apple Life was released. Honey Graham Life was introduced in early 2004, Life Vanilla Yogurt Crunch in late 2005, and another new flavor, Life Chocolate Oat Crunch, in 2006. All three were eventually discontinued in 2008. Finally, in 2008 Life introduced another new version, Maple & Brown Sugar Life. In Canada and certain areas of the United States, there is also Multigrain Life.

Original Life has been reformulated several times since its introduction. The most recent event took place in 1998, when Quaker introduced a "New and Improved

version. Consumer response was unfavorable, and Quaker quickly reverted to the original formula.

Nutrition[edit]

In 2010, Life was featured on the "Eat This, Not That" website. It was categorized as a healthy cereal but was negatively criticized for its content of the yellow food dye, Tartrazine.

QMRChex Mix is a type of snack mix that includes Chex breakfast cereal (sold by General Mills) as a major component. There are commercially sold pre-made varieties of Chex Mix, as well as many recipes (often printed on Chex cereal boxes) for homemade Chex Mix. Though contents vary, the mixes generally include an assortment of Chex cereals, chips, hard breadsticks, pretzels, nuts or crackers.

Not only are the chex quadrant grids but so are the pretzels

QMRChex Quest

From Wikipedia, the free encyclopedia

Chex Quest

Cover art from the game's original CD sleeve as found in boxes of Chex cereal in 1996.

Developer(s) Digital Café

Publisher(s) Digital Café

Producer(s) Virtual Communications[1]

Composer(s) Andrew Benson

Engine id Tech 1

Platform(s) MS-DOS

Microsoft Windows

Release date(s)

NA 1996

Genre(s) First-person shooter

Mode(s) Single-player

Multiplayer

Chex Quest is a non-violent first-person shooter video game created in 1996 by Digital Café as a Chex cereal promotion aimed at children aged 6–9 and up.[2][3] It is a total conversion of the more violent video game Doom (specifically The Ultimate Doom version of the game). Chex Quest won both the Golden EFFIE Award for Advertising Effectiveness in 1996[4][5] and the Golden Reggie Award for Promotional Achievement in 1998,[4][6] and it is known today for having been the first video game ever to be included in cereal boxes as a prize.[7][8] The game's cult following[9] has been remarked upon by the press as being composed of unusually devoted fans of this advertising vehicle from a bygone age.[10][11][12]

QMRScooby-Doo is an American animated cartoon franchise, comprising several animated television series produced from 1969 to the present day. The original series, Scooby-Doo, Where Are You!, was created for Hanna-Barbera Productions by writers Joe Ruby and Ken Spears in 1969. This Saturday-morning cartoon series featured four teenagers—Fred Jones, Daphne Blake, Velma Dinkley, and Norville "Shaggy" Rogers—and their talking brown Great Dane[1] named Scooby-Doo, who solve mysteries involving supposedly supernatural creatures through a series of antics and missteps.[2]

The fourth is always different. The fifth is ultra transcendent. It's a dog

QMRScooby-Doo (also known as Scooby-Doo: The Movie) is a 2002 American comedy horror mystery film. Based on the long-running Hanna-Barbera animated television series Scooby-Doo, the film was directed by Raja Gosnell, written by James Gunn and stars Freddie Prinze, Jr., Sarah Michelle Gellar, Linda Cardellini, Matthew Lillard and Rowan Atkinson. It is the first installment in the Scooby-Doo live-action film series.

The plot revolves around Mystery Incorporated, a group of four young adults and a dog who solve mysteries. After a two-year disbandment, the group reunites to investigate a mystery on a popular horror resort. Filming took place in and around Queensland on an estimated budget of $84 million

QMRA check (also checker, Brit: chequer) is a pattern of modified stripes consisting of crossed horizontal and vertical lines forming squares.

Etymology[edit]

The word is derived from the ancient Persian language word shah, meaning "king", from the oriental game of chess, played on a squared board, particularly from the expression shah mat, "the king is dead", in modern chess parlance "check-mate". The word entered the French language as echec in the 11th century,[1] thence into English.

Checks are quadrants

Use in fabrics[edit]

Check-patterned fabrics display bands in two or more colours in woven cloth. Checks are traditionally associated with Scotland where woven dyed wool was, at one time, a principal cloth. District checks were created as camouflage for moving inconspicuously on the laird's lands. The checks are associated with a specific area as opposed to the tartan of a family or clan. Checks are also used as distinctive patterns for woven cloth in modern designs.

Other uses[edit]

The check pattern is also used in many areas other than textile styles, for example: on a board used by the mediaeval Exchequer to perform financial computations, and on a board used for playing checkers and chess, and in heraldry.

QMRTartan is a pattern consisting of criss-crossed horizontal and vertical bands in multiple colours. Tartans originated in woven wool, but now they are made in many other materials. Tartan is particularly associated with Scotland. Scottish kilts almost always have tartan patterns. Tartan is often called plaid in North America, but in Scotland, a plaid is a tartan cloth slung over the shoulder as a kilt accessory, or a plain ordinary blanket such as one would have on a bed.

Tartan is made with alternating bands of coloured (pre-dyed) threads woven as both warp and weft at right angles to each other. The weft is woven in a simple twill, two over — two under the warp, advancing one thread at each pass. This forms visible diagonal lines where different colours cross, which give the appearance of new colours blended from the original ones. The resulting blocks of colour repeat vertically and horizontally in a distinctive pattern of squares and lines known as a sett.

The Dress Act of 1746 attempted to bring the warrior clans under government control by banning the tartan and other aspects of Gaelic culture. When the law was repealed in 1782, it was no longer ordinary Highland dress, but was adopted instead as the symbolic national dress of Scotland.

Until the middle of the nineteenth century, the highland tartans were only associated with either regions or districts, rather than any specific Scottish clan. This was because like other materials, tartan designs were produced by local weavers for local tastes and would usually only use the natural dyes available in that area, as chemical dye production was non-existent and transportation of other dye materials across long distances was prohibitively expensive.

The patterns were simply different regional checked-cloth patterns, chosen by the wearer's preference – in the same way as people nowadays choose what colours and patterns they like in their clothing, without particular reference to propriety. It was not until the mid-nineteenth century that many patterns were created and artificially associated with Scottish clans, families, or institutions who were (or wished to be seen as) associated in some way with a Scottish heritage.[1] The Victorians' penchant for ordered taxonomy and the new chemical dyes then available meant that the idea of specific patterns of bright colours, or "dress" tartans, could be created and applied to a faux-nostalgic view of Scottish history.

It is generally stated that the most popular tartans today are the Black Watch (also known as Old Campbell, Grant Hunting, Universal, Government), and the Royal Stewart.[2] Today tartan is no longer limited to textiles, but is used on non-woven mediums, such as paper, plastics, packaging, and wall coverings.[3]

Construction[edit]

Diagram A, the warp

Diagram B, the weft

Diagram C, the tartan. The combining of the warp and weft.

Each thread in the warp crosses each thread in the weft at right angles. Where a thread in the warp crosses a thread of the same colour in the weft they produce a solid colour on the tartan, while a thread crossing another of a different colour produces an equal mixture of the two colours. Thus, a sett of two base colours produces three different colours including one mixture. The total number of colours, including mixtures, increases quadratically with the number of base colours so a sett of six base colours produces fifteen mixtures and a total of twenty-one different colours. This means that the more stripes and colours used, the more blurred and subdued the tartan's pattern becomes.[6][9]

The sequence of threads, known as the sett, starts at an edge and either repeats or reverses on what are called pivot points. In diagram A, the sett reverses at the first pivot, then repeats, then reverses at the next pivot, and will carry on in this manner horizontally. In diagram B, the sett reverses and repeats in the same way as the warp, and also carries on in the same manner vertically. The diagrams left illustrate the construction of a "symmetrical" tartan. However, on an "asymmetrical" tartan, the sett does not reverse at the pivots, it just repeats at the pivots. Also, some tartans (very few) do not have exactly the same sett for the warp and weft. This means the warp and weft will have alternate thread counts.

Tartan is recorded by counting the threads of each colour that appear in the sett.[note 1] The thread count not only describes the width of the stripes on a sett, but also the colours used. For example, the thread count "K4 R24 K24 Y4" corresponds to 4 black threads, 24 red threads, 24 black threads, 4 yellow threads.[10] The first and last threads of the thread count are the pivot points.[3] Though thread counts are indeed quite specific, they can be modified in certain circumstances, depending on the desired size of the tartan. For example, the sett of a tartan (about 6 inches) may be too large to fit upon the face of a necktie. In this case the thread count has to be reduced in proportion (about 3 inches).[10

Colour: shades and meaning[edit]

The shades of colour in tartan can be altered to produce variations of the same tartan. The resulting variations are termed: modern, ancient, and muted. These terms refer to colour only. Modern represents a tartan that is coloured using chemical dye, as opposed to natural dye. In the mid-19th century natural dyes began to be replaced by chemical dyes which were easier to use and were more economic for the booming tartan industry. Chemical dyes tended to produce a very strong, dark colour compared to the natural dyes. In modern colours, setts made up of blue, black and green tend to be obscured. Ancient refers to a lighter shade of tartan. These shades are meant to represent the colours that would result from fabric aging over time. Muted refers to tartan which is shade between modern and ancient. This type of tartan is very modern, dating only from the early 1970s. This shade is said to be the closest match to the shades attained by natural dyes used before the mid-19th century.[11]

The idea that the various colours used in tartan have a specific meaning is purely a modern one. One such myth is that red tartans were "battle tartans", designed so they would not show blood. It is only certain recently created tartans, such as Canadian provincial and territorial tartans and American state tartans, that are designed with certain symbolic meaning for the colours used. For example, the colour green sometimes symbolises prairies or forests, blue can symbolise lakes and rivers, and the colour yellow is sometimes used to symbolise various crops.[2]

Tartan in fashion[edit]

A German punk wearing a piece of the Royal Stewart tartan, 1984.

In the Victorian and Edwardian eras, tartan-clad garments featured in fashion catalogues. By then, tartan had shifted from being mainly a component of men's clothing to become an important part of women's fashion. In consequence of its association with the British aristocracy and military, tartan developed an air of dignity and exclusivity. Because of this, tartan has made reappearances in the world of fashion several times. For instance, tartan made a resurgence in its use in punk fashion. In the late 1970s, punk music was a way for youth in the British Isles to voice their discontent with the ruling class. The unorthodox use of tartan, which had long been associated with authority and gentility, was then seen as the expression of discontent against modern society. In this way tartan, worn unconventionally, became an anti-establishment symbol.[54][55]

The world's first colour photograph, made by the Scottish scientist James Clerk Maxwell in 1861, was of a tartan ribbon.[23]

The chequered flag[edit]

"Chequered flag" and "Checkered flag" redirect to this section. For other uses, see Checkered Flag (disambiguation)

A typical chequered flag design

The chequered flag is displayed at the start/finish line to indicate that the race is officially finished. At some circuits, the first flag point will display a repeat chequered flag (usually on the opposite side of the circuit). The flag is commonly associated with the winner of a race, as they are the first driver to "take" (in other words, drive past) the chequered flag.

Upon seeing the chequered flag and crossing the finish line, drivers are required to slow to a safe speed, and return to their garage, parc ferme, or the paddock, depending on the applicable regulations of the series.

Design of the chequered flag[edit]

There is no standard design for the chequered flag. Although it nearly always consists of alternating black and white squares or rectangles arranged in a chequerboard pattern, the number, size, and length-width proportions of the rectangles vary from one flag to another. Also, the chequered flag typically has a black rectangle at the corner of the flag closest to the top of the flagpole. There have been instances of the black and white squares being painted onto a wooden board and simply held up for drivers to observe at the finish line. In events where Sunoco is the series fuel sponsor, the chequered flag often also has their logo emblazoned in the center of the flag, a practice that was used in NASCAR originally with Union 76, but is also used in IndyCar, since Sunoco's fuel sponsorship began. In NASCAR and F1 events, a single chequered flag is waved to signal the completion of a race. In IndyCar, two chequered flags are waved together, a tradition dating to the 1980 Indianapolis 500, but only if the race is under green conditions. (The starter will wave both a chequered and yellow flag if safety car conditions occur at the end of the race, in a yellow-chequer finish.)

NASCAR traditionally has a special version of the chequered flag sewn for Victory Lane that has the name and date of the race on it, a practice that Sunoco has spread to IndyCar since taking over its fuel sponsorship. That flag is used for the team in the winner's photographs taken after the race, and is a prize awarded to the team along with the race trophy. Teams often hang such flags at their headquarters in a similar fashion to other sports teams hanging championship banners from the rafters at stadiums.

Origins of the chequered flag[edit]

alt text

A chequered flag being used at the end of the 1906 Vanderbilt Cup

The exact origins of the use of a chequered flag to end races are unclear, although there are many theories. A possible though unlikely theory is that horse races during the early days of the settlement of the American Midwest were followed by large public meals and that to signal that the meals were ready and racing should come to an end, a chequered tablecloth was waved.

Another origin theory claims that the chequered flag's earliest known use was for 19th century bicycle races in France.[7]

A more likely explanation is that a high-contrast flag would be more conspicuous against the background of a crowd, especially when early races were run on dirt tracks (and therefore dust reduced the driver's visibility).

The earliest known photographic record of a chequered flag being used to end a race was from the 1906 Vanderbilt Cup race held in Long Island, New York.[8]

A 2006 publication The Origin of the Checker Flag: A Search for Racing's Holy Grail, written by historian Fred Egloff and published by the International Motor Racing Research Center at Watkins Glen, traces the flag's origin to one Sidney Waldon, an employee of the Packard Motor Car Company, who in 1906 devised the flag to mark "checking stations" (now called "checkpoints") along the rally-style events of the Glidden Tour.

In 1980, USAC starter Duane Sweeney started a tradition at the Indianapolis 500 by waving twin chequered flags at the end of the race. Previous starters had only used a single flag. Sweeney also marked the first use of twin green flags at the start of the race.[9][10]

Celebrating a win with the chequered flag[edit]

Late model stock car driver celebrates with a chequered flag

In snowmobile water cross the chequered flag is attached to the racer's life vest, and the racer is rewarded with a victory lap.

In many short tracks, the flagman gives the chequered flag to the winner of the race, but a variety of other celebratory traditions, such as the burnout, the Polish victory lap and the victory lane or victory circle celebration, sometimes overshadow the chequered flag tradition.

Use outside auto racing[edit]

The chequered flag has become so well recognized that it is often used to indicate the conclusion of many things unrelated to auto racing. For example, some software installation programs display a chequered flag to indicate that a computer program has been installed successfully.[citation needed]

Chequered flags were also posted at each corner of the end zones in the original Yankee Stadium when the facility was used by the New York Giants of the National Football League from 1956 through 1973.

The chequered flag is not only used for Auto Racing, but also for a representation of the automotive industry itself.

QMRSquare lattice

From Wikipedia, the free encyclopedia

Square lattices

Square Lattice.svg

Upright square

Simple diagonal square

Centered

Upright square tiling. The vertices of all squares together with their centers form an upright square lattice. For each color the centers of the squares of that color form a diagonal square lattice which is in linear scale √2 times as large as the upright square lattice.

In mathematics, the square lattice is a type of lattice in a two-dimensional Euclidean space. It is the two-dimensional version of the integer lattice, denoted as Z2.[1] It is one of the five types of two-dimensional lattices as classified by their symmetry groups;[2] its symmetry group in IUC notation as p4m,[3] Coxeter notation as [4,4],[4] and orbifold notation as *442.[5]

Two orientations of an image of the lattice are by far the most common. They can conveniently be referred to as the upright square lattice and diagonal square lattice; the latter is also called the centered square lattice.[6] They differ by an angle of 45°. This is related to the fact that a square lattice can be partitioned into two square sub-lattices, as is evident in the colouring of a checkerboard.

Symmetry[edit]

The square lattice's symmetry category is wallpaper group p4m. A pattern with this lattice of translational symmetry cannot have more, but may have less symmetry than the lattice itself. An upright square lattice can be viewed as a diagonal square lattice with a mesh size that is √2 times as large, with the centers of the squares added. Correspondingly, after adding the centers of the squares of an upright square lattice we have a diagonal square lattice with a mesh size that is √2 times as small as that of the original lattice. A pattern with 4-fold rotational symmetry has a square lattice of 4-fold rotocenters that is a factor √2 finer and diagonally oriented relative to the lattice of translational symmetry.

With respect to reflection axes there are three possibilities:

None. This is wallpaper group p4.

In four directions. This is wallpaper group p4m.

In two perpendicular directions. This is wallpaper group p4g. The points of intersection of the reflexion axes form a square grid which is as fine as, and oriented the same as, the square lattice of 4-fold rotocenters, with these rotocenters at the centers of the squares formed by the reflection axes.

QMRBattenburg markings or Battenberg markings are a pattern of high-visibility markings used primarily on the sides of emergency service vehicles in several European countries, Australia, New Zealand, and Hong Kong. The name comes from the similarity in appearance to the cross-section of a Battenberg cake.

They are quadrants

QMRArgyle (pattern)

From Wikipedia, the free encyclopedia

An example of an Argyle style pattern

An argyle (occasionally argyll) pattern is made of diamonds or lozenges. The word is sometimes used to refer to an individual diamond in the design but more commonly refers to the overall pattern. Most argyle layouts contain layers of overlapping motifs, adding a sense of three-dimensionality, movement, and texture. Typically, there is an overlay of intercrossing diagonal lines on solid diamonds.

The argyle pattern is derived from the tartan of Clan Campbell, of Argyll in western Scotland,[1] used for kilts and plaids, and from the patterned socks worn by Scottish Highlanders since at least the 17th century. (See illustrations in History of the kilt.) These were generally known as "tartan hose".[2][3]

Argyle knitwear became fashionable in Great Britain and then the USA after the first world war. Pringle of Scotland popularised the design, helped by its identification with the Duke of Windsor.[4] Pringle's website says that "the iconic Pringle argyle design was developed" in the 1920s.[5] The duke, like others, used this pattern for golf clothing: both for jerseys and for the long socks needed for the plus-fours trouser fashion of the day.

Payne Stewart (1957–1999), who won the U.S. Open and a PGA championship, was known and loved by fans for his bright and "flashy" dress; he wore tams, knickerbockers, and argyle socks.[6]

As a knitting pattern, argyle is generally accomplished using the intarsia technique. Argyle patterns are occasionally woven.

Some sports teams use bright, contemporary interpretations of the argyle pattern: for example, the Garmin-Slipstream professional cycling team, nicknamed the "Argyle Armada", and the Norwegian men's curling team at the 2010 Winter Olympics.[7] On April 27, 2013 the professional soccer team Sporting Kansas City of Major League Soccer (MLS) in the United States announced their third kit of the 2013 season featuring an argyle pattern.[8] The University of North Carolina has used the argyle pattern for its basketball uniforms since 1991, and introduced it as alternate for all sports uniforms in 2015. [9]

These are quadrants

QMRHarlequin print is a women's fashion design which was introduced by designer Adele Simpson in 1944. She presented the harlequin print in a bold diamond design on the town suits she created. It was also featured in green and white with a green jacket and a black skirt.[1]

It reflects quadrants

QMRTattersall (cloth)

From Wikipedia, the free encyclopedia

Blue and black checked tattersall cotton cloth.

Tattersall describes a check or plaid pattern woven into cloth. The pattern is composed of regularly-spaced thin, even vertical warp stripes, repeated horizontally in the weft, thereby forming squares.

The stripes are usually in two alternating colours, generally darker on a light ground.[1] The cloth pattern takes its name from Tattersall's horse market, which was started in London in 1766.[2] During the 18th century at Tattersall's horse market blankets with this checked pattern were sold for use on horses.[1]

Today tattersall is a common pattern, often woven in cotton, particularly in flannel, used for shirts or waistcoats. Traditional shirts of this cloth are often used by horseback riders in formal riding attire, and adorned with a stock tie.

QMRWarp (weaving)

From Wikipedia, the free encyclopedia

Warp and weft in plain weaving

In weaving cloth, the warp is the set of lengthwise yarns that are held in tension on a frame or loom. The yarn that is inserted over-and-under the warp threads is called the weft, woof, or filler. Each individual warp thread in a fabric is called a warp end or end.[1][2] Warp means "that which is thrown across" (Old English wearp, from weorpan, to throw, cf. German werfen, Dutch werpen).

Very simple looms use a spiral warp, in which a single, very long yarn is wound around a pair of sticks or beams in a spiral pattern to make up the warp.[3]

Because the warp is held under high tension during the entire process of weaving and warp yarn must be strong, yarn for warp ends is usually spun and plied fibre. Traditional fibres for warping are wool, linen, alpaca, and silk. With the improvements in spinning technology during the Industrial Revolution, it became possible to make cotton yarn of sufficient strength to be used as the warp in mechanized weaving. Later, artificial or man-made fibres such as nylon or rayon were employed.

While most people are familiar with weft-faced weavings, it is possible to create warp-faced weavings using densely arranged warp threads. In warp-faced weavings, the design for the textile is in the warp, and so all colors must be decided upon and placed during the first part of the weaving process and cannot be changed. Warp-faced weavings are defined by length-wise stripes and vertical designs due to the limitations of color placement. Many South American cultures, including the ancient Incas and Aymaras used a type of warp-faced weaving called backstrap weaving, which uses the weight of the weaver's body to control the tension of the loom. [4]

warp and weft are quadrant weaving

McNuggets are formed, not ground. There are 4 shapes that are pressed out with a rolling cookie cutter: boot, bow-tie, ball and bell. The reason they are all standard in shape and size is to ensure consistency in all McDonald’s restaurants. This guarantees both food safety (standard cooking times in restaurants) and portion control.

Fox)

For as long as I can remember, I’ve known that McDonald’s Chicken McNuggets came in only a handful of repeating shapes. But I’d never considered that the folks at the Golden Arches actually had specific names for each of the four types of McNugget.

Furthermore, the names are not science-y code numbers like A-V1X3 (which does sound tasty), but pretty much the same names you’d expect a 4-year-old to give to the McNugget shapes.

Thanks to the folks at Business Insider, who recently scored a trip to McDonald’s HQ outside of Chicago, we now know that those four shapes are indeed called: Boot (the one that looks like a boot; duh), Ball (the circular one; also duh), Bell (for the one that is sort-of teardrop shaped, and could resemble the silhouette of a bell), and Bone (the one with the least-defined shape; looks kind of like the Boot with the toe cut off).

(Apparently in Canada, the Bone is actually called Bow-Tie, probably because that’s slightly less unappetizing than the idea of eating an actual chicken bone.)

Kim Bhasin of Business Insider even posted this handy image you can print out and take to the McDonald’s with you next time you go:

QMRLandscapes of the Four Seasons (1486), Sesshū Tōyō. Ink and light color on paper.

QMRCeltic cross stitch is a style of cross-stitch embroidery which recreates Celtic art patterns typical of early medieval Insular art using contemporary cross-stitch techniques. Celtic cross stitch typically employs rich, deep colors, intricate geometrical patterns, spirals, interlacing patterns, knotwork, alphabets, animal forms and zoomorphic patterns, similar to the decorations found in the Book of Kells.

Although they share design inspirations, today's Celtic cross-stitch differs from the embroidery of the Celtic Revival of the late 19th and early 20th century which employed freehand surface embroidery stitches in line with the principles of the Arts and Crafts Movement (see art needlework).[1]

Celtic cross stitch embroideries are very much part of the heritage found in Scotland, Isle of Man and Ireland. These cross stitch patterns are used to decorate everyday items, such as cushion covers, wall tapestries and decorations, tea cozies, eyeglass covers and clothing.

QMRA trellis (treillage) is an architectural structure, usually made from an open framework or lattice of interwoven or intersecting pieces of wood, bamboo or metal that is normally made to support and display climbing plants, especially shrubs.[1] There are many types of trellis for different places and for different plants, from agricultural types, especially in viticulture, which are covered at vine training systems, to garden uses for climbers such as grapevines, clematis, ivy, and climbing roses or other support based growing plants. The rose trellis is especially common in Europe and other rose-growing areas, and many climbing rose varieties require a trellis to reach their potential as garden plants. Some plants will climb and wrap themselves round a trellis without much artificial help being needed while others need training by passing the growing shoots through the trellis and/or tying them to the framework.

Four Styles of Trellis-work

Trellis can also be referred to as panels, usually made from interwoven wood pieces, attached to fences or the roof or exterior walls of a building. A pergola usually refers to trellis-work that is laid horizontally above head height to provide a partial "roof" in a garden (pergolas are also used in agricultural settings).

It is made up of quadrants

QMRHolbein stitch is a simple, reversible line embroidery stitch most commonly used in Blackwork embroidery and Assisi embroidery. The stitch is named after Hans Holbein the Younger (1497-1543), a 16th-century portrait painter best known for his paintings of Henry VIII and his children, almost all of whom are depicted wearing clothing decorated with blackwork embroidery.

Although superficially similar to Back Stitch the Holbein stitch produces a smoother line and a pattern that is identical on both sides of the fabric. It can be worked in straight lines, diagonally, or in a stepped fashion to make a zigzag line and is well suited to creating outlines or intricate filling patterns.

Holbein stitch is also known as double running stitch, line stitch, Spanish stitch, Chiara stitch and two-sided line stitch.

Contents [hide]

1 Description of the technique

2 Modern Holbein techniques

3 Photo gallery

4 See also

5 References

Description of the technique[edit]

Holbein stitch is usually worked on on an even-weave fabric where the threads can be counted to ensure perfect regularity and is worked in two stages. Firstly, a row of evenly spaced running stitches is worked along the line to be covered. Then the return journey is completed, filling in the spaces between stitches made on the first journey and sharing the same holes:

The stitch looks like even quadrants

QMRThe lip and spur drill bit is a variation of the twist drill bit which is optimized for drilling in wood. It is also called the brad point bit or dowelling bit.

Conventional twist drill bits tend to wander when presented to a flat workpiece. For metalwork, this is countered by drilling a pilot hole with a spotting drill bit. In wood, the lip and spur drill bit is another solution: The centre of the drill bit is given not the straight chisel of the twist drill bit, but a spur with a sharp point and four sharp corners to cut the wood. The sharp point of the spur simply pushes into the soft wood to keep the drill bit in line.

Music chapter

QMRYoruba drums typically belong to four major families, which are used depending on the context or genre where they are played. The Dùndún / Gángan family, is the class of hourglass shaped talking drums, which imitate the sound of Yoruba speech. This is possible because the Yoruba language is tonal in nature. It is the most common and is present in many Yoruba traditions, such as Apala, Jùjú, Sekere and Afrobeat. The second is the Sakara family. Typically, they played a ceremonial role in royal settings, weddings and Oríkì recitation; it is predominantly found in traditions such as Sakara music, Were and Fuji music. The Gbedu family (literally, "large drum") is used by secret fraternities such as the Ogboni and royal courts. Historically, only the Oba might dance to the music of the drum. If anyone else used the drum they were arrested for sedition of royal authority. The Gbèdu are conga shaped drums played while they sit on the ground. Akuba drums (a trio of smaller conga-like drums related to the gbèdu) are typically used in afrobeat. The Ogido is a cousin of the gbedu. It is also shaped like a conga but with a wider array of sounds and a bigger body. It also has a much deeper sound than the conga. It is sometimes referred to as the "bass drum". Both hands play directly on the Ogido drum. Today, the word Gbedu has also come to be used to describe forms of Nigerian Afrobeat and Hip Hop music. The fourth major family of Yoruba drums is the Bàtá family which are well decorated double faced drums, with various tones. They were historically played in sacred rituals. They are believed to have been introduced by Shango, an Orisha, during his earthly incarnations as a warrior king. Traditional Yoruba drummers are known as Àyán. The Yoruba believe that Àyángalú was the first drummer. He is also believed to be the spirit or muse that inspires drummers during renditions. This is why some Yoruba family names contain the prefix 'Ayan-' such as Ayangbade, Ayantunde, Ayanwande.[94] Ensembles using the dundun play a type of music that is also called dundun.[89] The Ashiko (Cone shaped drums), Igbin, Gudugudu (Kettledrums in the Dùndún family), Agidigbo and Bèmbé are other drums of importance. The leader of a dundun ensemble is the oniyalu meaning; ' Owner of the mother drum ', who uses the drum to "talk" by imitating the tonality of Yoruba. Much of this music is spiritual in nature, and is often devoted to the Orisas.

Agogo metal gongs

Within each drum family there are different sizes and roles; the lead drum in each family is called Ìyá or Ìyá Ìlù, which means "Mother drum", while the supporting drums are termed Omele. Yoruba drumming exemplifies West-African cross-rhythms and is considered to be one of the most advanced drumming traditions in the world. Generally, improvisation is restricted to master drummers. Some other instruments found in Yoruba music include, but are not limited to; The Gòjé (violin), Shèkèrè (gourd rattle), Agidigbo (thumb piano that takes the shape of a plucked Lamellophone), Saworo (metal rattles for the arm and ankles, also used on the rim of the bata drum), Fèrè (whistles), Aro (Cymbal)s, Agogô (bell), different types of flutes include the Ekutu, Okinkin & Igba

QMRThe Cartan matrix of a rank r root system is an r × r matrix whose entries are derived from the simple roots. Specifically, the entries of the Cartan matrix are given by

A_{ij} = 2\frac{(\alpha_i,\alpha_j)}{(\alpha_i,\alpha_i)}

where (−,−) is the Euclidean inner product and αi are the simple roots. The entries are independent of the choice of simple roots (up to ordering).

The Cartan matrix for E8 is given by

\left [

\begin{smallmatrix}

2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 \\

-1 & 2 & -1& 0 & 0 & 0 & 0 & 0 \\

0 & -1 & 2 & -1 & 0 & 0 & 0 & 0 \\

0 & 0 & -1 & 2 & -1 & 0 & 0 & 0 \\

0 & 0 & 0 & -1 & 2 & -1 & 0 & -1 \\

0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 \\

0 & 0 & 0 & 0 & 0 & -1 & 2 & 0 \\

0 & 0 & 0 & 0 & -1 & 0 & 0 & 2

\end{smallmatrix}\right ].

The determinant of this matrix is equal to 1.

Dance chapter

QMRGridiron football, or North American football,[1] is a form of football primarily played in the United States and Canada.[2][3][4][5][6] The predominant forms of gridiron football are American football and Canadian football.

The term "gridiron" originated as a description of the sport's then-characteristic playing field, which, until the late 1910s–early 1920s, was marked with a series of parallel lines in a checkerboard (or grid) pattern, resembling a gridiron.[7] The grid system was abandoned in favor of the system of yard lines and hash marks used today, but the term "gridiron" has survived.

"Gridiron" football developed in the late 19th century out of the original games now known as rugby football and association football. It is distinguished from other football codes by its use of hard plastic helmets and shoulder pads, the forward pass, the system of downs, a line of scrimmage, more specialist positions and formations, free substitution, platooning of different players for offense and defense, measurements in yards, a distinctive brown leather ball in the shape of a prolate spheroid, and the ability to score points while not in possession of the ball by way of the safety. Walter Camp is credited with creating many of the rules that differentiate gridiron football from its older counterparts.

The international governing body for gridiron football is the International Federation of American Football (IFAF); although the organization uses the name "American football" and plays all of its international competitions under American rules, it uses a definition of the game that is broad enough that it includes Canadian football under its umbrella, and Football Canada (the governing body for Canadian football) is an IFAF member.

Grids are quadrants. The first football fields were originally explicitly made of quadrants.  The name gridiron has remained.

QMRDiagram of an American Football field (1904). The lines on the field originally made a checkerboard (or grid) pattern, which inspired the name "gridiron."

The term "gridiron" in reference to football first developed in the United States as a description of the sport's then-characteristic playing field, which originally was marked with a series of parallel lines in a checkerboard (or grid) pattern, resembling a gridiron.[7] The word "gridiron," in use since the 14th century, refers to a metal grid for cooking food over a fire, and derives from the same root as "griddle."[7]

As described in Outdoor Sports and Games (1911), by Claude H. Miller:—

A football field is 330 feet long by 160 feet wide. At each end are goal posts set 18 feet 6 inches apart, with a crossbar 10 feet above the ground. The field is marked off in chalk lines similar to a tennis court, these lines being 5 yards apart. The centre of the field where the play starts is 55 yards from either end. It is usually customary to run lines parallel to the sides of the field, also 5 yards apart, but as a field is but 160 feet wide the first and last of these lines are but 5 feet from the side lines instead of 5 yards. The lines on a football field make a checkerboard effect and have given to the field the name of "gridiron."

As a result, the name of the field, "gridiron," was applied to the game itself. The ball would be snapped in the grid in which it was downed on the previous play. The grid system was abandoned in favor of the system of yard lines and hash marks used today, but the term "gridiron" has survived.

Especially outside of the U.S. and Canada, the terms "gridiron" and "gridiron football" are often used to distinguish the North American sport from other codes of football. "Gridiron" is the normal word for the sport in Australia and New Zealand.[5][6][8] In some cases the terms are used specifically for American football, sometimes even in distinction from Canadian football,[9] though it is now often used as a blanket term for both North American variants.[3]

In the United States and Canada, the game is known unambiguously as football; the term gridiron is often used in a more poetic sense or for more colorful newspaper headlines. Association football is known in these countries as "soccer."

QMRA gridiron is a metal grate with parallel bars typically used for grilling meat, fish, vegetables, or combinations of such foods. It may also be two such grids, hinged to fold together, to hold food securely while grilling over an open flame.

It is a quadrant grid

Development[edit]

Early examples of the gridiron were found in Pompeii. The Latin term is "craticula", a diminutive form of "crates". This referred to their cross-hatched design, which appeared similar to a wicker basket, or crate.[1] This is also usedas the base for the term graticule, passing through French.[2]

There were numerous iron gridirons manufactured and patented in the U.S. in the 1800s. Originally called spiders, these iron legged devices were used in a fireplace placed over the fire to cook food. Over time, gridirons have been developed specifically to accommodate the type of food being prepared and the cooking method being used. A combination hinged gridiron and spider was developed and patented in 1836 by Amasa and George Sizer of Meriden, Connecticut.[3] A steel wire gridiron was developed and patented as early as 1889 in New Haven, Connecticut, by William C. Perkins, of the New Haven Wire Goods Co., who received a U.S. Patent #408,136 for a hinged gridiron that would hold the meat in place while broiling.[4] A commercial hinged broiler or gridiron was designed for use in the Bridge & Beach, Co., 1898 vertical cast iron stove. This hinged broiler was manufactured by Luigi Pieragostini, also of the New Haven Wire Goods Co., and patented in 1939; U.S. Patent #2,148,879.[5]

Today, hinged gridirons are used extensively to deep fry or broil fast food in restaurants throughout the world. Hotdog gridirons are also available for camping and outdoor cooking.

Cultural references[edit]

Gridirons are essential to Chapter 28 of David Copperfield when David, the Micawbers and Traddles improvise a meal on one. Dickens mentions them again as a suitable and practical gift for a blacksmith to make for someone in Charles Dickens' book Great Expectations where he refers to their use for cooking small fish known as "sprats".

The American football field resembles a gridiron, which brought up the term "gridiron football".

In Christian iconography the gridiron is an attribute of Saint Lawrence of Rome.

QMRA well-known legend has persisted from earliest times. As deacon in Rome, St Lawrence was charged with the responsibility for the material goods of the Church and the distribution of alms to the poor.[4] St Ambrose of Milan relates that when St Lawrence was asked for the treasures of the Church he brought forward the poor, among whom he had divided the treasure as alms.[5] "Behold in these poor persons the treasures which I promised to show you; to which I will add pearls and precious stones, those widows and consecrated virgins, which are the church’s crown."[1] The prefect was so angry that he had a great gridiron prepared, with coals beneath it, and had Lawrence’s body placed on it (hence St Lawrence's association with the gridiron). After the martyr had suffered the pain for a long time, the legend concludes, he made his famous cheerful remark, "I'm well done. Turn me over!"[4][7] From this derives his patronage of cooks and chefs, and also of comedians.

Some historians, such as Rev. Patrick Healy, view the traditions of how St Lawrence was martyred as "not worthy of credence",[8] as the slow lingering death cannot be reconciled "with the express command contained in the edict regarding bishops, priests, and deacons (animadvertantur) which ordinarily meant decapitation."[8] A theory of how the tradition arose is put forward by Pio Franchi de' Cavalieri, who postulates that it was the result of a mistaken transcription, the accidental omission of the letter "p" – "by which the customary and solemn formula for announcing the death of a martyr – passus est ["he suffered," that is, was martyred] – was made to read assus est [he was roasted]."[8] The Liber Pontificalis, which is held to draw from sources independent of the existing traditions and Acta regarding Lawrence, uses passus est concerning him, the same term it uses for Pope Sixtus II (martyred by beheading during the same persecution).[8]

Constantine I is said to have built a small oratory in honour of St Lawrence, which was a station on the itineraries of the graves of the Roman martyrs by the seventh century. Pope Damasus I rebuilt or repaired the church, now San Lorenzo fuori le Mura, while the minor basilica of San Lorenzo in Panisperna was built over the place of his martyrdom. The gridiron of the martyrdom was placed by Pope Paschal II in the church of San Lorenzo in Lucina.

The Escorial Palace, at the foot of Mount Abantos in the Sierra de Guadarrama, was built by King Philip II of Spain to commemorate the victory over King Henry II of France at the Battle of St Quentin, which took place on the feast of St Lawrence, 10 August 1557. To honour him, the floor of this imposing edifice was laid out in the form of a gridiron, the means by which St Lawrence was martyred.

St Lawrence is the patron saint of Ampleforth Abbey whose Benedictine monks founded one of the world's leading public schools for Catholics, located in North Yorkshire (North East England).

QMRSt Lawrence holding the gridiron, by the Master of Meßkirch, c.1535-40.

QMRA dance pad, also known as a dance mat, dance platform, flitter deck, or jitter deck is a flat electronic game controller used for input in dance games. Most dance pads are divided into a 3×3 matrix of square panels for the player to stand on, with some or all of the panels corresponding to directions or actions within the game. Some dance pads also have extra buttons outside of the main stepping area, such as "Start" and "Select". Pairs of dance pads are often joined side-by-side for certain gameplay modes.

Popular arcade games such as Dance Dance Revolution, In the Groove, and Pump It Up use large steel dance platforms connected to the arcade cabinet, whereas versions for home consoles usually use smaller (often flexible) plastic pads. These home pads are specifically made for systems such as the GameCube, Wii, Dreamcast (Japan only), PlayStation, PlayStation 2 and Xbox, but can also be used in computer simulators such as StepMania through the use of special adapters.

A dance pad is a quadrant grid with four options up, down, right, or left

Types[edit]

Soft[edit]

The 1987 Power Pad is a classic example of the soft pad.

"Soft" pads are thin and made of plastic. They generally cost $10–$20 USD. They are good for beginners to dance games or casual use, but they have a tendency to move around and wrinkle up during gameplay (unless "modded", such as by gluing or taping them to the top of a piece of plywood or the bottom of a transparent office chair mat). They are not usually durable and may wear out easily, but for light use they are quite suitable. Manufacturers of soft pads include Konami, BNSUSA, RedOctane, Intec, Mad Catz (Beat Pad), MyMyBox, Naki International, and Nintendo (Action Pad).[1] OEM manufacturers include Topway (manufacturer of RedOctane pads), Futime, and many others.

Some soft pads contain stiff foam inserts of the dense or hard varieties to provide more stability and durability. The inserts usually ship as three or six puzzle pieces (to allow for a smaller box) which fit together using a dovetail joint and slide into the dance pad, which then zips closed around the foam. Certain brands of foam pads put raised plastic sections under the directional buttons to allow them to be more easily felt by a player's feet, so as to help keep him centered on the pad. These pads generally cost between $40 and $100.

It is also possible to modify a pad by attaching it to a hard surface and optionally covering it with clear material; this can increase pad life and keep it from slipping around.

Hard[edit]

The arcade version of Dance Dance Revolution's two-player dance platform is an example of a hard pad.

"Hard" pads are usually constructed with metal (and sometimes wood) for durability, and usually come with a raised bar behind the player. Arcade machines use very durable metal pads that are designed for heavy use. Other hard pads can be purchased for home use with a video game system; the prices can be around US$100 to $350 ($200–$600 for double pads) - $700 to $1000+ online. Manufacturers of hard pads include DDRgame, Cobalt Flux, MyMyBox, Brown Box, RedOctane (ceased production as of February 2010 due to company termination) and Naki International.

Hard pads are used in all arcade versions of music games that employ dance pads, and often serve as the nec plus ultra for DIY Gamers that attempt to construct "Homebrew pads." Many Homebrew kits are ultimately instruction guides for converting soft pads into hard pads, although Homebrew hard pads often feature additional functions such as additional inputs (see below).

Solid State[edit]

A type of solid state dance pad

"Solid State" pads replace the usual mechanical switch and contact used in other hard pads. A proximity sensor is used to detect a player's steps on the pad. The advantages of a solid state design is that they do not require pressure to activate, eliminating moving parts that might break down and keeping dirt from getting into the mechanism.

Caveats[edit]

Problems are often encountered when attempting to use a PlayStation pad with a computer simulator. Most PlayStation-PC adapters will not register Up and Down, or Left and Right, simultaneously initially, although they are common "jumps" in dance games. This is because normal PlayStation games do not require such input, and because D-pads are not usually designed to physically permit such input. StepMania's website has a section concerning adapter compatibility.[2] Although these devices may work on a PC, to date, the adapters will not work with consoles that have built in USB ports such as the PlayStation 3 and the Xbox 360.

Purchasers of home pads should be aware of the number and arrangement of active arrow panels that are required by the game(s) they want to play. Although most commercial pads have four arrow panels (DDR/In The Groove), some have five (Pump It Up), six (Dance Dance Revolution Solo 2000), eight (Dance:UK), (MC Groovz Dance Craze), or nine (Technomotion).

Homebrew pads[edit]

Homebrew DDR pad

Not satisfied with the cost and/or reliability of factory assembled metal dance pads, many players construct their own dance pad. Using common materials (such as plywood, sheet metal, and acrylic glass or polycarbonate) found at local hardware stores), do-it-yourselfers are able to construct a pad that is often much more durable and more authentic-feeling than commercially built hard pads. Some homebrew pads have extra features such as additional arrows (for playing Pump It Up or DDR Solo), menu switches and pushbuttons, and bars. Furthermore, the homebrew pads are easier to repair because they use common parts, and are usually designed for easy disassembly.

While some homebrew pads use custom electronics built from scratch, most homebrew pads make use a circuit board from a standard controller to simplify the process of interfacing the pad with a gaming system. The controller used depends on the system that the pad is intended to be played with (GameCube, PlayStation, Xbox, or PC).

Homebrew pads use a variety of technologies for designing the arrows that the player is supposed to step on. The most common design uses metal contacts that sandwich together when the player steps on the pad or arcade button switches but some novel ideas have been proposed such as the use of optical, pressure, vibration, or proximity sensors.[3][4]

Due to the amount of work needed to create a custom metal pad, some players instead opt to modify their existing soft pads. Most of the time, players will take plywood sheets, acrylic, or even office chair floor protectors and staple it to their soft pads. This effectively cures wrinkling and makes the pad more durable to use while wearing shoes.[5]

QMRPump It Up (Hangul: 펌프 잇 업; RR: Peompeu it eop), commonly abbreviated as PIU or shortened to just Pump, is a music video game series developed by Nexcade and published by Andamiro, a Korean arcade game producer. The game is typically played on a dance pad with five arrow panels: up-left, up-right, bottom-left, bottom-right, and a center panel. Additional gameplay modes may utilize two five-panel pads side-by-side. These panels are pressed using the player's feet, in response to arrows that appear on the screen in front of the player. The arrows are synchronized to the general rhythm or beat of a chosen song, and success is dependent on the player's ability to time and position his or her steps accordingly.

The original version of the game was originally released in South Korea in August 1999. The game has also been released in other markets, such as North America and South America and in Europe. There are two current releases in the series. Pump It Up Fiesta 2 is the international version, and Pump It Up Infinity is an exclusive release to the United States, United Kingdom, and Canada. Pump it Up has tried to cater more to Freestyle players than "technical" players with more freestyle-friendly charts, as a result the game has more of a culture in the freestyle and Breakdancing disciplines. However, the game still caters well to technical players with a vast array of high difficulty songs and stepcharts.

It has four options dance steps top right top left bottom left bottom right

QMR Twister is a game of physical skill produced by Milton Bradley Company and Winning Moves. It is played on a large plastic mat that is spread on the floor or ground. The mat has four rows of large colored circles on it with a different color in each row: red, yellow, blue and green. A spinner is attached to a square board and is used to determine where the player has to put their hand or foot. The spinner is divided into four labeled sections: right foot left foot, right hand and left hand. Each of those four sections is divided into the four colors (red, yellow, blue and green). After spinning, the combination is called (for example: "right hand yellow") and players must move their matching hand or foot to a circle of the correct color. In a two-player game, no two people can have a hand or foot on the same circle; the rules are different for more players. Due to the scarcity of colored circles, players will often be required to put themselves in unlikely or precarious positions, eventually causing someone to fall. A person is eliminated when they fall or when their elbow or knee touches the mat. There is no limit to how many can play at once, but more than four is a tight fit.

The four rows are in a sort of quadrant formation of four colors

History and analysis[edit]

Twister was submitted for patent by Charles F. Foley and Neil Rabens in 1966, and became a success when Eva Gabor played it with Johnny Carson on television's The Tonight Show on May 3, 1966.[1][2] However, in its success, Twister was also controversial. The company that produced the game, Milton Bradley, was accused by its competitors of selling "sex in a box".[3] That accusation was probably because Twister was the first popular American game to use human bodies as playing pieces.[4]

Although Twister was patented by Foley and Rabens, a number of sources also mention Reyn Guyer.[5][6][7] Guyer is credited as having conceived Twister in its earliest form while working on a Johnson's Shoe Polish promotion as vice-president of his father's design company, the Reynolds Guyer Agency of Design. Guyer originally called this new game idea "Pretzel", but Milton Bradley changed the name to "Twister" before they put it on the market, much to Guyer's dismay.[8][9]

Co-inventor Charles Foley was a salesman for a printing company calling on the Guyer Company's purchasing agent when he saw a model of Kings' Footsie on display in the office. Foley went to Reyn claiming he had some experience and connections in the toy business. Guyer and his father discussed the possibility of starting a small division of the company to explore the ‘people are the players' concept. His father agreed to take out a sizable bank loan to underwrite the idea. Guyer hired Foley and Rabens and the three men worked together to develop eight new game ideas for presentation. The game ideas ranged from small kids' games to word games for adults. When the three men were working with colored circles on the floor, Foley suggested they place them in rows by color, and Rabens suggested they use their hands and feet. A game they called "Pretzel" took shape.

QMRA chess table is a table built with features to make it useful for playing the game of chess. A chess board is usually integral to the table top and often two drawers are provided to hold the pieces when not in use. Chess tables can be extremely decorative, well made and potentially expensive pieces of furniture. Most chess tables have the board inlaid or engraved though cheaper tables may have it painted on. A chess table is not necessary to play chess and is not restricted only to playing chess.

Chess tables are typically made of solid wood with rosewood, cedar, and mahogany being the most popular. Exotic wood versions are also available.

Many cities and universities have chess tables in their parks and gardens. Many coffeehouses also have chess tables. Most are the size of a normal picnic table, although some are larger than life sets that use pieces that are about the size of a small barrel.

The chess grid is the quadrant grid

QMRThe Matrix of Four Forms of Meditative Breath

Breath is the basis of all life. Breath is also the basis of all meditation and meditative movement. Breath is the primary manner in which we all obtain life energy. The other three in metaphysical understanding are water, food and prana or chi. The most important concept to understand about breath and meditative movement is that one moves in coordination with the breath. One moves in and out of postures with the breath and one deepens and lengthens postures in coordination with the breath. Inhalations equate to tension whereas exhalations equate to relaxation and release.

There are four important aspects of meditative breath. It is important to breathe slowly, deeply, steadily and consciously. It’s said most people breathe wrong. Most people breathe either from high, mid or low points. A complete yogi breath is a cyclical movement beginning from low point moving like a wave. Meditative movement leads to proper cyclical, complete breath.

Balanced breathing is utilized most frequently. Balanced breathing means the four parts to one breath cycle are equalized. The inhalations and exhalations are the same length of time to each other and the pause full and pause empty are the same length of time to each other too. For example 8 seconds in, 2 second pause, 8 seconds out, 2 second pause is an example of steady balanced breath. Meditation practitioners from long ago would count the breath not in seconds, but heartbeats.

With the nae nae dance the dancer does four counts after four steps backwards. Its four counts of freestyles

Literature chapter

The four forms of the in spanish are based off of a dichotomy of masculine and feminine and plural and singular they are la el las los

QMR Thomas Day's The History of Sandford and Merton, four volumes that embody Rousseau's theories

QMRLittle Women, a story about four sisters, is said to show power of women in the home and is seen as both conservative and radical in nature. The character of Jo is observed as having a rather contemporary personality and has even been pinned as a representation of the feminist movement.

Cinema chapter

QMRIn the previous post I walked through the examples provided in the book, which took a “day in the life” approach by focusing on a fictional executive named Linda. The basis for understanding the argument starts with platform theater – where one “scripts in advance every line and every gesture, practicing each over and over again until she can confidently give a performance so accomplished that it comes off as fresh and spontaneous.”

Platform theater represents the way many companies operate, from the most basic call center designs right through to the experience created for customers. It’s a comfortable way for many companies to operate, and relatively low-risk as well thanks to the controlled environment. But as anyone who’s taken Investing 101, it is through taking calculated risks that rewards are achieved.

So now let’s take a look at the definitions of more “evolved” forms of theater:

matching theater – where “disparate facts and events (are pieced) together (into) a unified whole, much like a film editor or director.”

street theater – where “small, atomic units of activity are called on demand to construct a performance.”

improv theater – where “surprising” problems must be handled immediately, and where Linda had to draw on “the reservoir of managerial techniques she has stored up from past experience.” The chapter notes that “Improv requires systematic and deliberate methods of originating creative ideas, fresh expressions, and new ways of addressing old problems.”

I would argue that various social media applications be be used to help move from “platform theater” to each of the other options. The most involved, of course, is “improv theater” – and here is where I think we could really dig into the opportunities that social media tools can create for companies. How much better could those “systematic and deliberate” methods be if wikis, blogs, social networks, reputation profiles, ranking systems, and the like where fully capitalized on? I also like the idea of taking improv theater to the next logical step – pulling customers on stage to participate in the experience directly (see: prosumerism).

So what do wikinomics readers think – would this be a useful framework to develop in relation to social media and customer experiences, and if so how might you go about expanding on it?

dynamic performance stable script is street theatre

stable performance stable script is platform theatre

dynamic performance dynamic script is improv theatre

dynamic performance stable script is matching theatre

QMRThe four forms of Yoga are – Karma Yoga, Bhakti Yoga, Jnana Yoga and Raja Yoga. Each of them is suited to a different temperament or approach to life. Each of them is briefly described below:

Details of The Four Forms of Yoga

Karma Yoga or the Yoga of action is first form of the four forms of yoga and the path chosen primarily by those of an outgoing nature. It purifies the heart by teaching you to act selflessly, without thinking of the reward. By detaching yourself from the fruits of your actions and offering them to God, you learn to sublimate the ego. To achieve this, it is helpful to keep your mind focused by repeating a mantra while engaged in any activity.

Bhakti Yoga is 2nd form of the four forms of yoga and the path of devotion, which appeases those who have an emotional nature. The Bhakti yogi is motivated chiefly by the power of love and sees God as the embodiment of love. Through prayer, worship and ritual he surrenders himself to God, channellising and transmuting his emotions into unconditional love or devotion. Chanting or singing the praises of God form a substantial part of Bhakti Yoga.

Jnana Yoga is 3rd form of the four forms of yoga and the Yoga of knowledge or wisdom. It is the most difficult path, requiring tremendous strength of will and intellect. Taking the philosophy of Vedanta, the Jnana yogi uses his mind to inquire into its own nature. Jnana Yoga leads the devotee to experience his unity with God directly by breaking the the veil of ignorance. Before practising Jnana Yoga, the aspirant needs to have integrated the lessons of the other yogic paths — for without selflessness and love of God, strength of body and mind, the search for self-realisation can become mere idle speculation.

Raja Yoga is last form of the four forms of yoga and the science of physical and mental control. Often called the royal road it offers a comprehensive method for controlling the waves of thought by turning our mental and physical energy into spiritual energy.

The Eight Limbs of Raja Yoga

Out of all the four forms of Yoga, it is Raja Yoga that is practical to implement in modern life. It consists of eight limbs that are a progressive series of steps or disciplines which purify the body and mind, ultimately leading the yogi to enlightenment. These eight limbs or disciplines are:

Yama: (Abstinences) Moral conduct, truthfulness, non-covetuousness.

Niyama: (Observances) of cleanliness contentment, self-discipline, study and self-surrender to God.

Asana: Right Postures.

Pranayama: (Breath control) Control of pran by regulating breathing processes of inspiration, expiration and retention of breath.

Dharna: (Concentration) Fixing the mind on one object at a place or point.

Pratyahar: (Sense withdrawal) Turning the senses inward and withdrawing them from external objects.

Dhyana: (Contemplation) or meditation. Keeping the mind fixed exclusively on one object or idea for sometime without any interruption.

Samadhi: (Self-realization) Super-conscious experience in trances where enlightenment or Union with self takes place. The first five steps are referred to as ‘Bahiranga’ (external) and the remaining three as ‘Antaranga ‘ (internal). These eight steps of Raja Yoga will transform your being into a higher state where you will have absolute control over your mind and body.