Post · 𑐴𑐶𑐟𑐶

Galaxy Map @galaxy_map@mastodon.social · 4 weeks ago

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Had a mathematician over for lunch today and I showed him some polygon decomposition results from my old Imperfect Congruence website.

https://gruze.org/tilings

He encouraged me to try to find a place to publish a paper describing my algorithm and suggested some journals. So possibly another longer term project.

Eg., here are two ways to decompose a 15-gon into 5 equirectangular triangles or 3 pentagons (plus rhombi).

#mathematics

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Galaxy Map @galaxy_map@mastodon.social · 4 weeks ago

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Some mathematicians are familiar with the ability to decompose even order regular polygons into rhombi but are not familiar with the ability to decompose any composite order regular polygon into smaller order regular polygons.

Galaxy Map @galaxy_map@mastodon.social · 4 weeks ago

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My algorithm can decompose regular polygons in several different ways, but it still misses some possibilities. Like this 24-gon with 24 triangles. Still a lot of mysteries in polygon decomposition.

A 𑐴𑐶𑐟𑐶 (hiti) is an ancient Newah urban water feature: a stepped, sunken courtyard with waterspouts and a central pool. These are fed through a remarkable network of pipes, reservoirs, and irrigation systems drawing water from mountain springs dozens of kilometres away. Every day, hundreds of people from the neighbourhood come to draw water, bathe, and exchange news. They are a unique and precious feature of Newa urban architecture through which neighbourhoods are created.

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