Affine Maps and Feuerbach'sTheorem
Metric Geometry
2017-11-28 v1 History and Overview
Abstract
We give an affine proof of Feuerbach's theorem, by constructing an explicit affine map which takes the nine-point circle of any given Euclidean triangle to the incircle and fixes the Feuerbach point. The proof is shown to be valid in any Hilbert plane which satisfies the parallel postulate.
Cite
@article{arxiv.1711.09391,
title = {Affine Maps and Feuerbach'sTheorem},
author = {Patrick Morton},
journal= {arXiv preprint arXiv:1711.09391},
year = {2017}
}
Comments
27 pages, 3 figures. This paper was written in 2009. The proof it discsusses has been generalized in the paper "Synthetic Foundations of Cevian Geometry III: The generalized orthocenter" by the author and Igor Minevich