Euclid and His Twentieth Century Rivals

Twentieth-century developments in logic and mathematics have led many people to view Euclid's proofs as inherently informal, especially due to his use of diagrams. In "Euclid and His Twentieth-Century Rivals", Nathaniel Miller discusses the history of such diagrams in Euclidean geometry, develops a formal system for working with them, and concludes that they can indeed be used rigorously. Miller also introduces a diagrammatic computer proof system, based on this formal system. This volume will be of interest to mathematicians, computer scientists, and anyone interested in the use of diagrams in geometry.