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arXiv · 1804.04024

Conway's doughnuts

Peter Doyle·Shikhin Sethi
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Abstract

Morley's Theorem about angle trisectors can be viewed as the statement that a certain diagram `exists', meaning that triangles of prescribed shapes meet in a prescribed pattern. This diagram is the case n=3 of a class of diagrams we call `Conway's doughnuts'. These diagrams can be proven to exist using John Smillie's holonomy method, recently championed by Eric Braude: `Guess the shapes; check the holonomy.' For n = 2, 3, 4 the existence of the doughnut happens to be easy to prove because the hole is absent or triangular.

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Peter Doyle, Shikhin Sethi. 2018-04-11. Conway's doughnuts. https://arxiv.org/abs/1804.04024

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