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Euclid and His Twentieth Century Rivals

Diagrams in the Logic of Euclidean Geometry

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.

119 pages | 6 x 9 | © 2007

Mathematics and Statistics

Philosophy: General Philosophy


"The author invites his readers to a fascinating survey in the history of diagrams, starting from Euclid’s Geometry."

Zentralblatt Math

Table of Contents

1. Background
2. Syntax and Semantics of Diagrams
3. Diagrammatic Proofs
4. Meta-mathematical Results
5. Conclusions
Appendix A: Euclid’s Postulates
Appendix B: Hilbert’s Axioms
Appendix C: Isabel Luengo’s DS1
Appendix D: A CDEG transcript

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