Geometry: Euclid and Beyond

Preliminary Booksellers Text: Do Not Use This book takes Euclid's "Elements" ad the starting point for a study of geometry from a modern mathematical perspective. To begin, the reader will become familiar with the content of Euclid's work, at least those parts which deal with geometry. At a second level, the book studies the logical structure of Euclid's presentation. Euclid's "Elements" has been regarded for more than two thousand years as the prime example of the axiomatic method. At the third level of reading, involving rather broader investigaions than the first two levels mentioned above, the author considers various mathematical questions and subsequent developments which arise naturally from Euclid's

Inhalt

1. Euclid's Geometry.- 2. Hilbert's Axioms.- 3. Geometry over Fields.- 4. Segment Arithmetic.- 5. Area.- 6. Construction Problems and Field Extensions.- 7. Non-Euclidean Geometry.- 8. Polyhedra.- Appendix: Brief Euclid.- Notes.- References.- List of Axioms.- Index of Euclid's Propositions.