Poncelet’s porism: a long story of renewed discoveries, I

  title={Poncelet’s porism: a long story of renewed discoveries, I},
  author={Andrea Del Centina},
  journal={Archive for History of Exact Sciences},
  • A. Centina
  • Published 2016
  • Mathematics
  • Archive for History of Exact Sciences
In 1813, J.-V. Poncelet discovered that if there exists a polygon of n-sides, which is inscribed in a given conic and circumscribed about another conic, then infinitely many such polygons exist. This theorem became known as Poncelet’s porism, and the related polygons were called Poncelet’s polygons. In this article, we trace the history of the research about the existence of such polygons, from the “prehistorical” work of W. Chapple, of the middle of the eighteenth century, to the modern… Expand
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Poncelet plectra: harmonious curves in cosine space
  • D. Jaud, D. Reznik, Ronaldo Garcia
  • Mathematics, Computer Science
  • Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
  • 2021
It has been shown that the family of Poncelet N-gons in the confocal pair (elliptic billiard) conserves the sum of cosines of its internal angles, and that when N=3, the cosine triples of both families sweep the same planar curve: an equilateral cubic resembling a plectrum (guitar pick). Expand
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We study algebraic curves that are envelopes of families of polygons supported on the unit circle T. We address, in particular, a characterization of such curves of minimal class and show that allExpand
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We investigate closed chains of conics which carry Poncelet triangles. In particular, we show that every chain of conics which carries Poncelet triangles can be closed. Furthermore, for $$k=3$$k=3Expand
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It is shown that despite a more complicated dynamic geometry, the locus of certain triangle centers and associated points remain conics and/or circles. Expand
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Abstract In this note we provide two extensions of a particular case of Poncelet theorem.


I. On the porism of the in-and-circumscribed polygon
  • A. Cayley
  • Mathematics
  • Proceedings of the Royal Society of London
  • 1862
The Porism referred to is as follows, viz. two conics may be so related to each other, that a polygon may be inscribed in the one, and circumscribed about the other conic, in such manner that anyExpand
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