Quadri-Figures in Cayley-Klein Planes: All Around the Newton Line
Metric Geometry
2024-09-27 v1
Abstract
The Newton line and the associated theorems by Newton and Gauss for tetragons and quadrilaterals are closely linked to some other theorems of Euclidean geometry: a theorem by Bocher on the existence of a nine-point conic of a quadrangle, a theorem by Shatunov and Tokarev, and a theorem by Anne. This paper examines to which extent all these theorems can be transferred to other metric planes, in particular the elliptic and hyperbolic planes.
Keywords
Cite
@article{arxiv.2409.17802,
title = {Quadri-Figures in Cayley-Klein Planes: All Around the Newton Line},
author = {Manfred Evers},
journal= {arXiv preprint arXiv:2409.17802},
year = {2024}
}
Comments
22 pages / 16 figures