Geometry: Euclid and Beyond

by Robin Hartshorne

This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants, with complete proofs. Topics include the introduction of coordinates, the theory of area, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra.

Genres: Mathematics, Geometry, Science, Nonfiction, Textbooks

540 pages, 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.