Poncelet's porism

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Poncelet's porism in geometry states the following: Let C and D be two plane conics. If it is possible to find, for a given n > 2, one n-sided polygon which is simultaneously inscribed in C and circumscribed around D, then it is possible to find infinitely many of them.

Poncelet's porism can be proved via elliptic curves; geometrically this depends on the representation of an elliptic curve as the double cover of the projective line with four ramification points. The relevant ramification is where the conics intersect (at four points by Bézout's theorem).

It is named after French engineer and mathematician Jean-Victor Poncelet.

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