Poncelet's closure theorem

Poncelet's closure theorem states that if you draw a polygon inside a pair of carefully arranged, non-intersecting curves called conics (such as ellipses), and if one such polygon closes after a certain number of sides, then starting from any point on the outer conic will also produce a polygon that closes after the same number of steps. In simpler terms, once you find one polygon that fits perfectly inside both curves and comes back to its starting point, then the process will work from any starting point, creating infinitely many such polygons.