Conway’s Circle Theorem: a short proof, enabling generalization to polygons
Files
Accepted manuscript
Date
2021-11-02
DOI
Authors
Braude, Eric
Version
Accepted manuscript
OA Version
Citation
E. Braude. "Conway’s Circle Theorem: A Short Proof, Enabling Generalization to Polygons." CSECS-2020: 16th Annual International CSECS Conference on Computer Science and Education in Computer Science. Sofia, Bulgaria, 2021-09-18 - 2021-09-18. https://arxiv.org/abs/2111.01835.
Abstract
John Conway’s Circle Theorem is a gem of plane geometry: the six points formed by continuing the sides of a triangle beyond every vertex by the length of its opposite side, are concyclic. The theorem has attracted several proofs, even adorned Mathcamp T-shirts. We present a short proof that views the extended sides as equal tangents of the incircle, a perspective that enables generalization to polygons.
Description
License
© The Author(s) 2021. Open Access. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.