The altitudes of a triangle
History and Overview
2024-04-01 v1
Abstract
A long-standing, unanswered question regarding Euclid's Elements concerns the absence of a theorem for the concurrence of the altitudes of a triangle, and the possible reasons for this omission. In the centuries following Euclid, a remarkable number of proofs have been put forward; this suggests a search for the most elementary and direct proof. This paper provides a simple, direct, elementary proof of the theorem; it is based solely on the Elements.
Cite
@article{arxiv.2403.19670,
title = {The altitudes of a triangle},
author = {Mark Mandelkern},
journal= {arXiv preprint arXiv:2403.19670},
year = {2024}
}