Rebin Muhammad
Ohio University Mathematics graduate student Rebin Muhammad contributed a paper to a session on “My Favorite Math Circle Problem” at MathFest 2017, held July 26-29 in Chicago.
Muhammad’s problem was “Islamic Geometric Pattern.”
Abstract: An Islamic geometric pattern (IGP) is a 2D wallpaper that is created by using only a compass and a ruler. The history of IGPs date back to the 8th century and IGPs have been seen in most Islamic countries, where they have been used to decorate building walls and mosques. For the Math Circle session, we reconstruct one of these patterns, the “Seal of Solomon,” from scratch. Each student creates a tile and at the end of the session, we tile all of them into a single, decorated wall. Can we have different tilings? And why does the tiling work? What kind of symmetries do the tiles exhibit? Can you use the same construction line to create a different tile and are you sure that the lines between tiles are such that your design will tile the wall? In the second pattern, “Ten Chain,” students use modular arithmetic to construct the tile and to learn about Z10. We ask questions like: Can you generalize this example? Can you create “5 Chain, 6 Chain, etc.” ? What kind of chain cannot be constructed? This is followed by investigations of “interlacing” including when the strategy of interlacing works and the relationship between two neighboring chains.
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