# Conway's doughnuts

• Published in 2018
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.

### 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}
}