V. Poncelet proved in 1822 the following theorem. Let C and D be two plane conics. If it is possible to find, for a given n, one n-sided polygon which is simultaneously inscribed in C and circumscribed around D, then it is possible to find infinitely many of them. I will give two different proofs and describe analogies with an apparently unrelated problem. The question of why this theorem is called a 'porism' will be left unaddressed.
The talk should be accessible to Snooki.