girih

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Designed and produced byJane Chang Mei Qi

Special thanks toNanci Takeyama

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the author.

Copyright © 2010 by Jane Chang

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GIRIHA MANUAL TO THE MEDIEVAL ISLAMIC ART TILING SYSTEM.

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Islamic art encompasses the visual arts produced from the 7th century onwards by people (not necessarily Muslim) who lived within the territory that was inhabited by culturally Islamic populations. It includes fields as varied as architecture, calligraphy, painting, and ceramics, among others.

Typically, though not entirely, Islamic art has focused on the depiction of patterns and Arabic calligraphy, rather than on figures, because it is feared by many Muslims that the depiction of the human form is idolatry and thereby a sin against Allah, forbidden in the Qur’an.

MEDIEVAL ISLAMIC ART.

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Unlike the strong tradition of portraying the human figure in Christian art, Islamic art is often associat-ed with the arabesque style. Early Islam forbade the painting of human beings, including the Prophet, as Muslims believe this tempts followers of the Prophet to idolatry.

ARABESQUE.

A prohibition against depicting representational images in religious art, as well as the naturally decorative nature of Arabic script, led to the use of calligraphic decorations, which usually involved repeating geometrical patterns that expressed ideals of order and nature. It was used on religious architecture, carpets, and handwritten documents.

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As a result, Islamic art throughout history has been abstract and decorative, portraying geometric, floral, arabesque, and calligraphic designs. Today we see the presence of Koranic Arabic, used for reading and prayer, and for decoration, as the foremost characteristic of Islamic religious art, wherever it is found in the world and among every race.

The “Word of God” was recorded on a book known as the Qur’an (“recitation”), which is a compilation of Muhammad’s revelations. To transcribe Muhammad’s revelations, Arabic was adopted as the uniform script wherever Islam spread, and the very act of transcribing the Qur’an became sacred. It is expressed in the ancient Arabic proverb “Purity of writing is purity of the soul”.

To accomplish this holy duty, scribes developed Arabic calligraphy, the art of writing, to an extraordi-nary degree. Calligraphers draw from the Qur’an or proverbs as art, using the flowing Arabic language to express the beauty they perceived in the words of Muhammad.

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Medieval Islamic designers used elaborate geometrical tiling patterns to form beautiful and highly complexed architectural pieces, at least 500 years before Western mathematicians developed the concept.

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GIRIHTILES.

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The geometric design, called “girih”, was widely used to decorate Islamic buildings but the advanced mathematical concept within the patterns was not recognised, until now. Physicist Peter Lu at Har-vard University in Cam-bridge, Massachusetts, US, realised the 15th-century tiles formed so-called Pen-rose geometric patterns, when he spotted them on a visit to Uzbekistan.

Scholars had thought the girih were created by draw-ing a zigzag network of lines with a straight edge

and compass. But when Lu looked at them, he recognised the regular but non-repetitive patterns of Penrose tiling - a concept developed in the West only in the 1970s.

This set of Girih tiles con-sists of five tiles that were used in the creation of til-ing patterns for decoration of buildings in Islamic ar-chitecture. They are known to have been used since about the year 1200 and their arrangements found significant improvement starting with the Darb-i Imam shrine in Isfahan in Iran built in 1453.

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GIRIH IS THE PERSIAN WORD FOR “KNOT”.

THEY REFER TO THE SMALLER SUBDIVIDED TRIANGULAR PIECES WITHIN THE FIVE TILES.

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CAN YOU TELL WHICH GEOMETRIC SHAPES THERE ARE?

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THE FIVEGIRIH TILES.

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THE FIVEGIRIH TILES.

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a bow tie (non-convex hexagon) with interior angles of

72°, 72°, 216°, 72°, 72°, 216°

a rhombus with interior angles of

72°, 108°, 72°, 108°

a regular pentagon with five interior angles of 108°

ONE TWO THREE FOUR FIVE

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a regular decagon with ten interior angles of 144°

an elongated (irregular convex) hexagon with interior angles of 72°, 144°, 144°, 72°, 144°, 144°

ONE TWO THREE FOUR FIVE

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π/5

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There are five underlying shapes that account for the geometric complexity of their designs: a decagon, a pentagon, a hexagon, a rhombus and a “bowtie.” Although these are not immediately visible, they form the basis for the most complex, or “knotty,” girih designs.

These five basic shapes are regarded as the tools that enabled craftsmen to construct highly complex patterns over large surfaces without gaps or disruptions in their symmetry.

All sides of these figures have the same length; and all their angles are multiples of 36° (π/5). All of them, except the pentagon, have bilateral (reflection) symmetry through two perpendicular lines. Some have additional symmetries. Specifically, the decagon has tenfold rotational symmetry (rotation by 36°); and the pentagon has fivefold rotational symmetry (rotation by 72°).

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The girih tiles make possible large-scale patterns because each edge has the same length, allowing different combinations to be aligned. What is more, every edge is intersected at its midpoint by two decorating lines at fixed angles, which ensures that the lines continue across the edges from one tile onto another.

A further innovation was achieved by dividing girih tiles into smaller ones to create overlaid patterns at two different scales, a method mathematicians call “self-similarity transformation.” This kind of subdivision, combined with the symmetry imposed by the shapes of the girih tiles, creates non-periodic tiling.

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PERIODICITY.Most uses of girih tiles in Islamic architecture were periodic; they

had unit cells which were repeated in the same orientation within a lattice. Some had patterns which could not be extended to a tiling of the entire plane. None of them are known to have had patterns

which could be extended to the entire plane only in an aperiodic way.

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Subdiving Girih tiles into smaller ones, forming intricately beautiful and exquisite geomet-rical artworks.

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However, on some buildings, the large girih tiles were decorated with patterns which formed small girih tiles.

And on one of these, Darb-i Imam, the subdivision into smaller tiles was done in a way that could have been generalized to an aperio-dic tiling of the plane.

SUBDIVISION.

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“Perhaps the most striking innovation arising from the application of girih tiles was the use of self-similarity transformation (the subdivision of large girih tiles into smaller ones) to create overlapping patterns at two different length scales, in which each pattern is generated by the same girih tile shape,” says Lu.

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THE COLOURPALETTE.In Islamic art, the intensity of colors can vary greatly, although there are several basic conventions dictating how they are used. Bright and livid tones were inscribed in geometric patterns on the insides of buildings - never the outside.

The traditional instrument of the Arabic calligrapher is the qalam, a pen made of dried reed; the ink is often in color, and chosen such that its intensity can vary greatly, so that the greater strokes of the compositions can be very dynamic in their effect.

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TRY COLOURING IN AND ADDING YOUR OWN DETAILS!

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WHAT TO DONow it is time for you to have a go at creating these beautiful works of art. In the next brown envelope, you will find some transparencies with the pattern on it. See if you can match them with the following two famous Girih works.

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Cover of a Mamluk copy of the Qur’anEarly 14th century

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Abbasid al-Mustansiriyya Madrasa in Baghdad, IraqBetween 1227 and 1234

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WHAT TO DOWith the new skills that you have developed, you can now make your own art works with these provided Girih stickers! If you are up for more of a challenge, try to tessellate the tiles so that the Girih lines form the following patterns.

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“ We can’t say for sure what it means. It could be proof of a major role of mathematics in medieval Islamic art or it could have been justa way for artisans to construct their art moreeasily. It would be incredible if it were all coincidence. At the very least, it shows us a culture that we often don’t credit enough was far more advanced than we thought before.

”– Peter Lu, on his breakthrough discovery of the Girih tiles.

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We can’t say for sure what it means. It could be proof of a major role of mathematics in medieval Islamic art or it could have been justa way for artisans to construct their art moreeasily. It would be incredible if it were all coincidence. At the very least, it shows us a culture that we often don’t credit enough was far more advanced than we thought before.

girih

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