Geometry: Euclid and Beyond (Undergraduate Texts in Mathematics) by Robin Hartshorne

by Robin Hartshorne

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.- Brief Euclid.- Notes.- References.- List of Axioms.- Index of Euclid's Propositions.

Genres: Mathematics, Geometry, Science, Nonfiction, Textbooks

Hardcover

First published January 1, 2000

Reviews

[Parsa]

The first chapter examines Euclid chapter by chapter, hinting at the gaps in his proofs(starting from the first proposition, how do we know that the two circles actually meet? or the fourth proposition, how do we justify the method of superposition?)
The second chapter offers a modern look on Euclid, using Hilbert's axioms. Some of these axioms are modern re-interpretations of Euclid's axioms, while some were not mentioned in Euclid, and some are actually theorems in Euclid(SAS is taken as an axiom in Hilbert's system) Using these axioms, we can recover Euclid, with some reinterpretations, and some alternative proofs.

[Diem · Rating 5 out of 5]

Not really fair to say I read this. I used the intro and first chapter for guidance through the first four books of Euclid's "Elements". This would be a rigorous and interesting text book for a geometry student. I can see why it is considered one of the best of its class.