A Property of Parallelograms Inscribed in Ellipses

DOI10.1080/00029890.2007.11920483zbMath1140.51010OpenAlexW2406491609WikidataQ58272979 ScholiaQ58272979MaRDI QIDQ5448060

Don Zagier, Alain Connes

Publication date: 20 March 2008

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00029890.2007.11920483

zbMATH Keywords

billiardsinscribedballisticsMonge's theoremconfocalorthopticellipse, parallelogram

Mathematics Subject Classification ID

Elementary problems in Euclidean geometries (51M04) Inequalities and extremum problems in real or complex geometry (51M16)

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The Birkhoff-Poritsky conjecture for centrally-symmetric billiard tables ⋮ Estimating elliptic billiard invariants with spatial integrals ⋮ Finiteness theorems on elliptical billiards and a variant of the dynamical Mordell–Lang conjecture ⋮ Moduli spaces of bicentric quadrilaterals ⋮ Can the elliptic billiard still surprise us? ⋮ Minimal Perimeter Parallelograms Inscribed in a Pair of Confocal Ellipses ⋮ Parallelograms inscribed in a pair of confocal ellipses ⋮ Dan Reznik's identities and more ⋮ Poncelet plectra: harmonious curves in cosine space

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