Geometry Euclid and Beyond

In recent years, I have been teaching a junior-senior-level course on the classi­ cal geometries. Students are expected to read concurrently Books I-IV of Euclid's text, which must be obtained sepa­ rately. And in the last chapter we provide what is missing from Euclid's treatment of the five Platonic solids in Book XIII of the Elements. 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. Also included are complete proofs, introduction of coordinates, the theory of area, geometrical constructions and finite field extensions, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra. The text is intended for junior-senior level mathematics majors. Robin Hartshorne is a professor of mathematics at the University of California, Berkeley, and is the author of "Foundations of Projective Geometry" (Benjamin, 1967) and "Algebraic Geometry" (Springer, 1977).