Cairo Tiling, Math Art

Pavement of the outside world. The Guardian: The unexpected beauty of manhole covers around the world – in pictures, 2015.

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graphic of a repeating pattern of an irregular pentagon in four colors.

Cairo tiling is a mathematical tesseract based on paving stones in Cairo. (I think, see below.)

The Internet abounds with graphic examples of Cairo tiling. Photos of the source pavement were harder to find.

Research Gate: My Undercover Mission to Find Cairo Tilings, Frank Morgan 2019. Restricted. I could see photo previews on my desktop, and in the search hits on my phone. Was able to open the PDF.

Facebook: Williams College 2019. Photos of Morgan with pavings. I was able to see the entry without logging in to FB. YMMV

Frank Morgan: Pentagons Everywhere 2011. Open. Photos interesting but not as directly relevant.

Note from the rabbit hole. Wiki: Cairo pentagonal tiling, cited by all of the Cairo tiling sites I read.

Process Notes

My goal was to understand Cairo tiling and draw a pattern. Got one; didn’t get the other. Tiling discussions get esoteric quickly. I still cannot grok how to generate a correct shape. The above was produced by closely following a set of steps. Medium: Cairo Tiling with no math, Ebbs 2020.

My one victory was to figure out how to draw this on the computer without having to use layers. I should figure out layers on Inkscape. I use them all the time in GIMP for photos. Meanwhile, my computer work for this was a festival of color variation. selecting, copying, grouping, ungrouping, and so on.

Onwards!
Katherine

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