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Twentieth-century developments in logic and mathematics have led
many people to view Euclid's proofs as inherently informal,
especially due to the use of diagrams in proofs. In "Euclid and His
Twentieth-Century Rivals," Nathaniel Miller discusses the history
of 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.
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