In search of a measure in poncelet’s porism

Cieślak, Waldemar; Mozgawa, Witold

doi:10.1007/s10474-016-0620-3

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2017

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“…This easily proves Poncelet's Theorem. A similar construction has been proposed by Bryant (2010), and Cieślak and Mozgawa (2016) found a nice geometric interpretation of the corresponding measure on the inscribed conic. Vallès (2012) devised a new proof of Poncelet's Porism and of the related Darboux Theorem based upon vector bundles by exploiting a link between Schwarzenberger bundles and Poncelet curves.…”

Section: Introductionmentioning

confidence: 54%

Closed chains of conics carrying poncelet triangles

Halbeisen¹,

Hungerbühler²

2017

Beitr Algebra Geom

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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 and k = 4 we show that there are closed chains of pairwise conjugate conics which carry Poncelet k-gons such that the contact points of each k-gon are the vertices of the next k-gon-such miraculous chains of conics do not exist for 5 ≤ k ≤ 23.

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Section: Introductionmentioning

confidence: 54%