Algebraic Methods in Plane Geometry.

`Riders' in geometry are always a pleasure to tackle , and this pleasure is doubled when on e finds connections between plane geometry and algebra . This three -part article is about such connection s. In Parts 1 and 2 , we explore some connections between plane geometry and the algebra of conics and cubics; in P art 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. [ABSTRACT FROM AUTHOR]