# 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.

## Links

## Other information

- key
- Conwaysdoughnuts
- type
- article
- date_added
- 2018-11-04
- date_published
- 2018-09-14

### 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 = {2018-09-14}, 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} }