Albrecht Hess, Daniel Perrin, and Mehdi Trense,
A group theoretic interpretation of Poncelet's theorem -- the real case,
Forum Geometricorum, 16
(2016) 381--395.
Abstract. Poncelet's theorem about polygons that are inscribed in a conic and at the same
time circumscribe another one has a greater companion, in which the second conic is
substituted by possibly different conics for different sides of the polygon, while all conics
belong to a fixed pencil. Here, a construction is presented that gives a visual group
theoretic interpretation of both theorems and, eventually, leads to a generalization
exposing the role of commutativity in Poncelet's theorem. There is no new thing
about the ingredients but we hope that a dynamical view sheds new light on them.
Finally, the occurrence of conics in a Poncelet grid [14] of lines constructed on a pencil of circles
is explained with a simple proof.
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