Algebraic methods in plane geometry

‘Riders’ in geometry are always a pleasure to tackle, and this pleasure is doubled when one finds connections between plane geometry and algebra. This three-part article is about such connections. In Parts 1 and 2, we explore some connections between plane geometry and the algebra of conics and cubics; in Part 1 we give algebraic proofs of results such as Pascal’s Theorem and the Butterfly Theorem, and in Part 2 we study some group theoretic and number theoretic aspects of cubic curves. In Part 3 we look at the role of mappings and transformation groups in plane geometry.