English

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