Sunday, October 04, 2020

When "tiling the plane" on a household floor pattern, you need "The Infinite Pattern that Never Repeats"

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The Infinite Pattern that Never Repeats”, a presentation by Paul Steinhardt on the problem of “tiling the plane” to infinity” (as in flooring), on the Versatium channel. Indeed, what a geometry lesson. 

The concept is called “Penrose tiling”, which I will defer to Wikipedia for explanation.  A related problem is how “quasi crystals” form in nature.

The picture above shows a typical mineral quasicrystal in nature, Wikipedia embed (click for attribution and chemical formula).

One can certainly imagine board or computer games based on this mathematics. Kadi Runnels explains how tiling can he used to explain the speed of light and relativity here

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