On Cusps of Caustics by Reflection: Billiard Variations on the Four Vertex Theorem and on Jacobi’s Last Geometric Statement

DOI10.1080/00029890.2023.2179842zbMath1515.78004arXiv2112.07852WikidataQ122966765 ScholiaQ122966765MaRDI QIDQ6042558

Gil Bor, Sergei Tabachnikov

Publication date: 11 May 2023

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

Full work available at URL: https://arxiv.org/abs/2112.07852

Mathematics Subject Classification ID

Geometric optics (78A05) Classical differential geometry (53Axx)

Related Items (1)

Open problems on billiards and geometric optics

Cites Work

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• Caustics through the looking glass
• Jacobi's lectures on dynamics. Delivered at the University of Königsberg in the winter semester 1842--1843 and according to the notes prepared by C. W. Borchardt. Edited by A. Clebsch. Translated from the original German by K. Balagangadharan. Translation edited by Biswarup Banerjee
• The heat equation shrinking convex plane curves
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• Global properties of spherical curves
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• The cut loci and the conjugate loci on ellipsoids
• The conjugate locus on convex surfaces
• Topological problems of the theory of wave propagation
• Jacobi’s last geometric statement extends to a wider class of Liouville surfaces
• Using Rolling Circles to Generate Caustic Envelopes Resulting from Reflected Light
• Introducing projective billiards
• On the Last Geometric Statement of Jacobi
• The Inverse Caustic Problem
• Combinatorics of fronts of Legendrian links and the Arnol'd 4-conjectures
• Variations on the Tait-Kneser theorem

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