Conway's doughnuts

• Published in 2018
• Added on 2018-11-04

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.

Links

• http://arxiv.org/abs/1804.04024v1
• http://arxiv.org/pdf/1804.04024v1

Other information

BibTeX entry

@article{Conwaysdoughnuts,
	key = {Conwaysdoughnuts},
	type = {article},
	title = {Conway's doughnuts},
	author = {Peter Doyle and Shikhin Sethi},
	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.},
	comment = {},
	date_added = {2018-11-04},
	date_published = {2018-09-26},
	urls = {http://arxiv.org/abs/1804.04024v1,http://arxiv.org/pdf/1804.04024v1},
	collections = {Food,Fun maths facts,Geometry},
	url = {http://arxiv.org/abs/1804.04024v1 http://arxiv.org/pdf/1804.04024v1},
	year = 2018,
	urldate = {2018-11-04},
	archivePrefix = {arXiv},
	eprint = {1804.04024},
	primaryClass = {math.HO}
}