Overview

During the nineteenth century several mathematicians realized, at about the same time, that a geometry based on Euclid's classic system was not the only possibility. A non-Euclidean universe was too strange for many to accept at first. Yet it was non-Euclidean geometry that paved the way for Albert Einstein's theory of general relativity in the early 1900s and the modern understanding of space-time.

Background

Geometry is one of the oldest branches of mathematics. Because it deals with the properties of objects and space, such as lengths, areas, volumes, and angles, it was of immediate practical significance. Ancient artists, artisans, engineers, architects, warriors, navigators, and astronomers all had objects to measure and build, courses to plot, or trajectories to predict.

The familiar geometry of planes and solids that most modern students learn...