Janos Bolyai, Non-Euclidean Geometry, and the Nature of Space

Rating:
Summary: alternatives to Euclid
Review: For some 2000 years, Euclid's postulates of geometry were considered the final word. As axioms, they seemed unassailable. Yet this neat little book describes how one mathematician stumbled on equally valid alternatives. Gray shows how Bolyai started by looking at Euclid's most controversial axiom. That two parallel lines in a plane will not intersect. An alternative formulation of which is that the angles of a triangle will always sum to pi radians.

Bolyai was able to show that by replacing this axiom, he could derive other self consistent geometric systems. One of which was inadvertantly already well known - the geometry of the surface of a sphere.

Gray goes on to show how this became the mathematical percursor to Einstein's theory of relativity, and our deeper understanding of space-time.