Poncelet

Poncelet is a French surname. The most notable bearer is Jean-Victor Poncelet (1788–1867), a French engineer and mathematician renowned for his foundational contributions to projective geometry and the theory of conics. His work helped unify classical results and laid the groundwork for the modern study of geometry. He also held positions in the French military engineering corps and influenced the training of engineers in the 19th century.

Poncelet's porism is a classical result in projective geometry named after him. It concerns polygons that are simultaneously inscribed in one conic and circumscribed about another conic. The porism states that if a polygon with a fixed number of sides closes for one starting point, then a closed polygon exists for any starting point, and in fact infinitely many such polygons exist. The theorem can be stated in its most general form for two conics, not necessarily circles, describing a closure property for a family of polygons or, equivalently, for billiard-type trajectories between conics.

The surname Poncelet, and in particular his porism, has left a lasting mark on geometry and its modern extensions. In mathematical literature, the name is associated with closure phenomena in conic settings and with the broader study of projective and synthetic geometry, influencing both classical results and contemporary research in related areas.