Poncelet theorems

W. Barth; Th. Bauer

Home/Archive/arXiv

arXiv · alg-geom/9502017

Poncelet theorems

W. Barth·Th. Bauer

View original source ↗Read source document ↗Export metadata ↓

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 $P_3$ (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.

Explore related subjects

alg-geom math.AG

Keep this discovery

BibTeX RIS

W. Barth, Th. Bauer. 1995-02-16. Poncelet theorems. https://arxiv.org/abs/alg-geom/9502017

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2015

Quotients par des groupes non réductifs et variétés de modules de complexes

I give a way to construct moduli spaces of complexes, as quotients of open subsets of the space of all complexes by the product of the groups of automorphisms of the terms.

alg-geom↗

arXiv2014

Plane Curves with Hyperbolic and C-hyperbolic Complements

The general problem which initiated this work is: What are the quasiprojective varieties which can be uniformized by means of bounded domains in $\cz^n$ ? Such a variety should be, in particular, C--hyperbolic, i.e. it should have a Carathéodory hyperbolic covering. We study here the plane projective curves whose complements are C--hyperbolic. For instance, we show that most of the curves whose duals are nodal or, more generally, immersed curves, belong to this class. We also give explicit examples of irreducible such curves of any even degree d greater or equal 6.

alg-geom↗

arXiv2014

Iitaka-Severi's Conjecture for Complex Threefolds

We prove the following generalization of Severi's Theorem: Let $X$ be a fixed complex variety. Then there exist, up to birational equivalence, only finitely many complex varieties $Y$ of general type of dimension at most three which admit a dominant rational map $f$ from $X$ to Y$.

alg-geom↗