English

Poncelet theorems

alg-geom 2025-04-09 v1 Algebraic Geometry

Abstract

If there is one polygon inscribed into some smooth conic and circumscribed about another one, then there are infinitely many such polygons. This is Poncelet's theorem. The aim of this note is to collect some (mostly classical) versions of this theorem, namely: - Weyr's Poncelet theorem in P3P_3 (1870), - Emch's theorem on circular series (1901), - Gerbaldi's formula for the number of Poncelet pairs (1919), - the Money-Coutts theorem on three circles (1971), - the zig-zag theorem (1974), - a (probably new) Poncelet theorem on three conics, - a Poncelet formula for quadrics of revolution.

Keywords

Cite

@article{arxiv.alg-geom/9502017,
  title  = {Poncelet theorems},
  author = {W. Barth and Th. Bauer},
  journal= {arXiv preprint arXiv:alg-geom/9502017},
  year   = {2025}
}

Comments

20 pages, LaTeX