Conway's doughnuts
History and Overview
2018-04-12 v1 Metric Geometry
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.
Keywords
Cite
@article{arxiv.1804.04024,
title = {Conway's doughnuts},
author = {Peter Doyle and Shikhin Sethi},
journal= {arXiv preprint arXiv:1804.04024},
year = {2018}
}