Isometric Billiards in Ellipses and Focal Billiards in Ellipsoids

zbMath1476.51014arXiv2105.05295MaRDI QIDQ5164368

Hellmuth Stachel

Publication date: 11 November 2021

Full work available at URL: https://arxiv.org/abs/2105.05295

zbMATH Keywords

causticconfocal quadricsconfocal conicsfocal axisbilliard in ellipsebilliard motioncanonical parametrizationPoncelet gridfocal billiard in ellipsoids

Mathematics Subject Classification ID

Surfaces in Euclidean and related spaces (53A05) Differential geometric aspects in kinematics (53A17) Elementary problems in Euclidean geometries (51M04) Geometric constructions in real or complex geometry (51M15) Dynamical systems with singularities (billiards, etc.) (37C83)

Related Items (3)

The geometry of billiards in ellipses and their Poncelet grids ⋮ On the motion of billiards in ellipses ⋮ Poncelet plectra: harmonious curves in cosine space

Cites Work

• Unnamed Item
• More about areas and centers of Poncelet polygons
• Geometry of integrable billiards and pencils of quadrics
• Orthogonale Erzeugendenpolygone auf einschaligen Hyperboloiden
• ``Knowledge gained by experience: Olaus Henrici -- engineer, geometer and maker of mathematical models
• Billiards in ellipses revisited
• The Universe of Conics
• The Universe of Quadrics
• On a Discretization of Confocal Quadrics. A Geometric Approach to General Parametrizations
• Algebra of operators on the ring of polytopes and quasi-symmetric functions

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