Parallelograms inscribed in a pair of confocal ellipses
type: Item
instance of: scholarly article
title: Parallelograms inscribed in a pair of confocal ellipses
zbMATH Open document ID: 1445.51005
DOI: 10.4171/EM/382
author: Dorota Blinkiewicz
author: Piotr Rzonsowski
author: B. Szydło
published in: Elemente der Mathematik
publication date: 2020-07-29T00:00:00Z
review text: In [Am. Math. Mon. 114, No. 10, 909--914 (2007; Zbl 1140.51010)], \textit{A. Connes} and \textit{D. Zagier} proved the following result for a pair of confocal ellipses \(E\) and \(E'\): Given any diameter \(AC\) of \(E\), there is a unique diameter \(BD\) of \(E'\), such that the parallelogram \(ABCD\) has maximum girth, and the value of this girth is independent of the diameter \(AC\). The original proof relies on analytical ideas, while the present work is devoted to provide a purely elementary geometrical proof. In passing, the authors introduce some other interesing results such as the Coxeter-Greitzer lemma or a generalization of a classical theorem by Monge.
Mathematics Subject Classification ID: 51M04
zbMATH DE Number: 7225566
zbMATH Keywords: confocal ellipses
reviewed by: Antonio M. Oller Marcén
MaRDI profile type: Publication
cites work: A Property of Parallelograms Inscribed in Ellipses
cites work: Q5550848
cites work: Safe domain and elementary geometry
full work available at URL: https://doi.org/10.4171/em/382
OpenAlex ID: W2937248315
description: scientific article; zbMATH DE number 7225566