Euclidean and Non-Euclidean Geometries

What's so sacred about parallel lines? Students and general readers who want a solid grounding in the fundamentals of space would do well to let M. Helena Noronha's Euclidean and Non-Euclidean Geometries be their guide. Noronha, professor of mathematics at California State University, Northridge, breaks geometry down to its essentials and shows students how Riemann, Lobachevsky, and the rest built their own by re-evaluating the parallel postulate. Each chapter devotes itself to rigorous study of one topic: neutral geometry, Euclidean 3-space, hyperbolic geometry, and more reveal themselves to the reader through the author's clear analyses and proofs. Problem sets help the student become comfortable with techniques and reach the conclusions through their own work, gaining a visceral understanding impossible through passive reading. Little mathematical background is needed beyond a bit of set theory, calculus, and a willingness to persevere. --Rob Lightner