If a polygon inscribed in one conic and circumscribed about another closes up after n steps for one starting point, it closes up after n steps for every starting point on the first conic. Proved by Jean-Victor Poncelet, it is a foundational porism of projective and algebraic geometry.
Facts
StatementIf one n-sided polygon can be found that is simultaneously inscribed in one conic section and circumscribed about another, then infinitely many such polygons exist, with every point of either conic serving as a vertex or tangency point of one of them. 1 Proof YearThe triangular case was found earlier, in 1746, by William Chapple; Poncelet's general closure theorem for polygons of any number of sides dates to 1822. Classification
Statement Form Connections
Sources
1. Poncelet's Closure Theorem (Wikipedia)
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It is named after French engineer and mathematician Jean-Victor Poncelet, who wrote about it in 1822; however, the triangular case was discovered significantly earlier, in 1746 by William Chapple.
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