# Conway's doughnuts

- Published in 2018
- Added on

In the collections

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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### BibTeX entry

@article{Conwaysdoughnuts, title = {Conway's doughnuts}, 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.}, url = {http://arxiv.org/abs/1804.04024v1 http://arxiv.org/pdf/1804.04024v1}, year = 2018, author = {Peter Doyle and Shikhin Sethi}, comment = {}, urldate = {2018-11-04}, archivePrefix = {arXiv}, eprint = {1804.04024}, primaryClass = {math.HO}, collections = {food,fun-maths-facts,geometry} }