Poncelet triangles: a theory for locus ellipticity

DOI10.1007/s13366-021-00620-0zbMath1496.51006arXiv2106.00715OpenAlexW4205942056MaRDI QIDQ2170456

Dominique Laurain, Dan Reznik, Mark Helman, Ronaldo A. Garcia

Publication date: 5 September 2022

Published in: Beiträge zur Algebra und Geometrie (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.00715

zbMATH Keywords

ellipsetriangle centerPoncelet

Mathematics Subject Classification ID

Questions of classical algebraic geometry (51N35) Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.) (68T20) Elementary problems in Euclidean geometries (51M04) Euclidean analytic geometry (51N20)

Related Items (1)

Loci of 3-periodics in an Elliptic Billiard: why so many ellipses?

Cites Work

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• Centers of mass of Poncelet polygons, 200 years after
• Circumcenter of mass and generalized Euler line
• More about areas and centers of Poncelet polygons
• Poncelet's closure theorem
• Can the elliptic billiard still surprise us?
• Billiards in ellipses revisited
• Dan Reznik's identities and more
• Loci of 3-periodics in an Elliptic Billiard: why so many ellipses?
• On the circumcenters of triangular orbits in elliptic billiard
• On the incenters of triangular orbits on elliptic billiards
• Invariant center power and elliptic loci of Poncelet triangles
• Bicentennial of the Great Poncelet Theorem (1813–2013): Current advances
• Poncelet Porisms and Beyond
• Family Ties
• New Properties of Triangular Orbits in Elliptic Billiards
• The Ballet of Triangle Centers on the Elliptic Billiard
• Elliptic Billiards and Ellipses Associated to the 3-Periodic Orbits

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