Constructing the cover of Issue 10

Chalkdust

10 December 2019

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Ever since Chalkdust Issue 10 was released in October we’ve been admiring the beautiful cover, which features artwork created by Samira Mian. Samira is inspired by patterns from Islamic geometry, which use simple compass and ruler constructions to create intricate tiles that can be repeated in a variety of ways. This article from Issue 10 discusses the history of patterns in Islamic geometry, and their connection to modern mathematics. If you’re curious about how these patterns are formed, and want to try constructing one yourself, Samira has shared with us a step-by-step guide to constructing the tile that forms the basic unit of the cover image, inspired by the Persian architect and geometer Ali Reza Sarvdalir.

Constructing the tile

Start with a sheet of A4 paper. Later, you will trace the tile onto A5 and repeat the pattern on larger A3. The first step is to draw a circle of radius 7cm, and then follow the instructions below:

Congratulations! You have now constructed the basic tile. The highlighted lines are the important ones for the pattern on the cover of Issue 10.

Repeating the tile

There are a couple of different ways that you can repeat this construction to make a larger image. One option is to trace the whole tile onto a larger sheet of tracing paper, and then valley-fold the tracing paper to produce a reflected copy. This can be reflected again vertically to make a 2-by-2 pattern seen on the Great Mosque in Damascus.

The reflected tile (left) and an example of it on the Great Mosque in Damascus (right — image by David Wade.)

Alternatively, you can trace half of the tile (the lower-right triangle) and reflect that. By combining 6 of these triangular tiles you can obtain a hexagonal pattern, which is the basis of the cover art for Issue 10. Happy constructing!

Combining the reflected triangular tile to make a hexagonally-symmetric pattern.

The cover of Issue 10, featuring the hexagonal pattern.