Poncelet's porism: a long story of renewed discoveries. I

DOI10.1007/s00407-015-0163-yzbMath1333.01015OpenAlexW1659036303MaRDI QIDQ907761

Andrea Del Centina

Publication date: 26 January 2016

Published in: Archive for History of Exact Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00407-015-0163-y

zbMATH Keywords

projective geometryPoncelet's closure theoremPoncelet's polygonsPoncelet's porism\((2,2)\)-correspondences

Mathematics Subject Classification ID

History of mathematics in the 18th century (01A50) History of mathematics in the 19th century (01A55) General theory of linear incidence geometry and projective geometries (51A05) Projective analytic geometry (51N15) Pencils, nets, webs in algebraic geometry (14C21)

Related Items (16)

Poncelet property and quasi-periodicity of the integrable Boltzmann system ⋮ Boscovich's geometrical principle of continuity, and the ``mysteries of the infinity ⋮ Brianchon and Poncelet's joint memoir, the nine-point circle, and beyond ⋮ Closed chains of conics carrying Poncelet triangles ⋮ The recognition and the constitution of the theorems of closure ⋮ Poncelet-Darboux, Kippenhahn, and Szegő: interactions between projective geometry, matrices and orthogonal polynomials ⋮ Estimating elliptic billiard invariants with spatial integrals ⋮ Poncelet’s theorem for conics in any position and any characteristic ⋮ Decomposable Blaschke products of degree 2ⁿ ⋮ Pascal's mystic \textit{hexagram}, and a conjectural restoration of his lost treatise on conic sections ⋮ Quiz 1: What color was George Washington's white horse? The mathematical version ⋮ On two extensions of Poncelet theorem ⋮ Unnamed Item ⋮ Carnot's theory of transversals and its applications by Servois and Brianchon: the awakening of synthetic geometry in France ⋮ Loci of Poncelet triangles in the general closure case ⋮ Poncelet plectra: harmonious curves in cosine space

Uses Software

• Wikibase

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• The rise of Cayley's invariant theory (1841--1862)
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• Variations on a theorem of Abel
• A Poncelet theorem in space
• On Cayley's explicit solution to Poncelet's porism
• Modular curves and Poncelet polygons
• Hidden harmony -- geometric fantasies. The rise of complex function theory
• Classical Algebraic Geometry
• Bicentennial of the Great Poncelet Theorem (1813–2013): Current advances
• Poncelet Porisms and Beyond
• Worlds Out of Nothing
• The British development of the theory of invariants (1841–1895)
• Poncelet’s Poristic Polygons

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