How did Islamic geometric patterns evolve?

Geometry of the Orient

"Whoever chooses a path to gain knowledge, God will make the path to paradise easier for him."

Koran

Geometric ornaments in Arab mosques seem to be based on a few basic figures, which, when cleverly arranged, result in aesthetic and complex patterns. The materials on this page allow you to work with these ornaments at various levels of difficulty.

Table of contents "Geometry of the Orient"

introduction

Ideas for teaching
- Idea 1: print out and colorize
- Idea 2: Cut out the building blocks and assemble them yourself into a pattern
- Idea 3: Arrange the building blocks on the computer to form new patterns

materials

Continue on the Internet
- German language pages
- English language pages

back to the "overview of gifted and gifted funding"

introduction

During a visit to Uzbekistan, the physicist Peter Lu discovered astonishing things while looking at the ornamental decorations of a mosque: The ornaments all seemed to consist of a few building blocks on the base of the pentagon.

The building blocks discovered by Peter Lu are:

Thanks to the clever arrangement of these five basic elements, thousands of ornaments seem to have been created from the 13th century onwards. Depending on the interior design of the individual building blocks, further variants developed, some of them with regular structures, others show non-repetitive patterns like those of thePenrose tiling (Wikipedia) are known.

Back to the table of contents "Geometry of the Orient"

Ideas for teaching

The ideas for the lessons are intended to give interested parties an easy introduction to working with geometric ornaments from the Arab culture. However, further ideas may also develop from the proposed activities.

Idea 1: print out and colorize

A first step is to print out and then color the samples listed in the Materials section. Different coloring techniques can be used. If the samples are used in their original size, the use of colored pencils has proven itself.

Colored pencil drawings look particularly beautiful when the individual areas and partial areas are not simply painted evenly, but also differentiated. Possibilities for this are:

  • Gradient of color or brightness
  • additional micro-elements such as the doubling of lines or patterns within the partial areas
  • Colors that go beyond the individual elements and thus make other structures visible

Detail from a colored pencil drawing

Before coloring, it is worthwhile to think about the choice of color.

  • Which colors should be used?
  • Which elements are colored how?
  • Should large-area elements be further differentiated?

So that the colors do not smear when inking, we recommend using an additional sheet that can be placed under the hand.

Coloring on the computer using suitable image processing is also possible.

Detail from a pattern edited on the computer

The color fill tool, which is available in most modern image processing systems, is suitable for coloring on the computer.

Back to the table of contents "Geometry of the Orient"

Idea 2: Cut out the building blocks and assemble them yourself into a pattern

Developing your own ornament is just as appealing as coloring an existing pattern. To do this, enough individual parts are first carefully cut out and then glued together piece by piece on a new sheet of paper.

Danger! Not all combinations that can be laid fill an area without any gaps. Anticipatory action is a prerequisite for success. The simplest are ornaments that are rotationally symmetrical because you can work with them from the inside to the outside. Ornaments that only appear to contain repetitions are much more demanding, as it often becomes apparent after some work that the corresponding parts can no longer be placed without gaps.

Either a glue stick or white glue should be used to glue the parts. Because the fingers inevitably become stickier and stickier, the hands have to be washed from time to time. You shouldn't wait too long before sticking the individual parts on, as a nicely laid ornament can be destroyed by a single draft.

If ornaments are glued by hand, it is clear that the precision of the ornaments put together on the computer cannot be achieved. Minor inaccuracies lead to the fact that individual parts overlap slightly (which can be corrected by trimming the parts) or that there are gaps between the parts. The second problem is less noticeable when the parts are glued onto a black piece of paper.

Coloring the glued-on parts is rather difficult with a colored pencil, as they like to stand up at the edges. Alternatively, the parts to be cut out can be copied onto colored paper beforehand; coloring after gluing is then no longer necessary.

However, it is also possible to trace or copy a preserved ornament onto another sheet before it is colored.

Detail from a glued-on ornament

The time required for the work depends on the size of the ornament to be developed. The time it takes to cut out the parts should not be underestimated.

If a child is still too young to glue the ornament himself, he or she can give instructions to an adult.

Back to the table of contents "Geometry of the Orient"

Idea 3: Arrange the building blocks in new patterns on the computer

If using scissors or glue is difficult or not fun, ornaments can also be developed on the computer with the help of the basic building blocks. Using the example of the free software OpenOffice Draw, it should be shown how.

The following techniques must be mastered:

  • opening the template file
  • saving the template file under a different name
  • copying and pasting graphic objects
  • moving graphic objects with the mouse
  • rotating graphic objects by a fixed angle (36 °)
  • printing out documents or PDF export

The individual techniques are explained step-by-step in the document Instructions for Creating Patterns in OpenOffice Draw.

The self-developed ornaments can be printed out for others. It is also possible to send it as a PDF by e-mail.

Back to the table of contents "Geometry of the Orient"

materials

Assorted components (PDF, 1 page A4)

Assorted components (PDF, 5 pages A4)

Example 1: Work of an eight-year-old girl (PDF, 1 page A4)

Example 2a: Work of a nine-year-old boy (PDF, 1 page A4)

Example 2b: Ornament dyed by the boy's grandmother (PDF, 1 page A4)

Example 3: ornament created by the author and colored on the computer (PDF, 1 page A4)

Example 4: ornament glued together by father and child (PDF, 1 page A4)

Ornament template 1 (PDF, 1 page A4)

Ornament template 2 (PDF, 1 page A4)

Ornament template 3 (PDF, 1 page A4)

Ornament template 4 (PDF, 1 page A4)

Ornament template 5 (PDF, 1 page A4)

Ornament template 6 (PDF, 1 page A3)

Ornament template 7 (PDF, 1 page A4)

Instructions for creating patterns in OpenOffice Draw (PDF, 9 pages A4)

File with basic elements for OpenOffice Draw (OpenOffice ODG, 1 page A4)

Back to the table of contents "Geometry of the Orient"

Continue on the Internet

Anyone interested in further information on the topic will find what they are looking for on the Internet. Most of the texts, however, are written in English.

German-language sources

Mosque builders were 500 years ahead of Western mathematicians at SpiegelOnline

Infinity Puzzle from Time

English language sources

Peter Lu's Discovery at Havard University: Short article on Lu's mathematical discovery

Islamic Architecture: Decagonal and Quasi-Crystalline Tilings in Medieval: Original article by Peter Lu in Science Vol. 315, 2007

Islamic Patterns: Book review showing another way to design oriental patterns

A Discovery in Architecture at MuslimHeritage: An article on the topic with additional links

Taprats - Computer Generates Islamic Star Patterns: Another possibility to generate patterns based on Islamic models

Islamic Art and Geometric Design - Learning Activities: Book for an exhibition at the Metropolitan Museum of Art

Islamic Based Geometric Design: Page with some picture examples

Islamic Art and Architecture: Page with background articles and examples on Islamic architecture and art

Islamic and Middle Eastern Art: Introductory text with many picture examples and further links

Historical and Geographical Connections for Tessellations and Tilings: Islamic Art and Tiling of Surfaces

Tessellation Database: Images by various artists

Islamic Lattice Creator: Interactive Java applet for creating your own ornaments

Tilings from Historical Sources: Images of numerous historical examples

Comments, suggestions and corrections to [email protected] are welcome.

Matthias Giger, February 2006 (Update: 07.03.2007)
www.gigers.com