Type: Seminar

Distribution: World

Expiry: 30 Mar 2010

Auth: pamelag(.ampgrad;1539.16000)@p80724.pc.maths.usyd.edu.au

In projective geometry, Pascal’s theorem states that if an arbitrary hexagon is inscribed in any conic section, and pairs of opposite sides are extended until they meet, the three intersection points will lie on a straight line. Pascal’s theorem is a special case of the Cayley–Bacharach theorem, a statement about a pencil of cubics through nine points. We will examine the proofs of these theorems, as well as their relations to classical configurations in Euclidean geometry.