Postgraduate Seminar: Ivan Guo -- From the Hexagons of Pascal to the Cubics of Cayley–Bacharach

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.