A Group Theory Proof of Pascal's Theorem

Abstract

It will be shown that Pascal's Theorem is equivalent to the associativity of a natural binary operation on conic sections. A novel proof for Pascal's Theorem will then be given by showing that this binary operation is associative independent of Pascal's Theorem. Specifically, this operation is equivalent to either addition of real numbers, multiplication of real numbers, or rotations on the plane depending on the type of the conic. Since each of these is already known to be associative, it will follow that the binary operation is associative and this will prove Pascal's Theorem.