Geometry and the Imagination

A wider readership than specialists is the aim of Geometry and the Imagination, the English translation of the German Anschauliche Geometrie, written by David Hilbert with Stefan Cohn-Vossen and based on lectures Hilbert gave in the winter of 1920 and 1921. The authors distinguish a tendency toward abstraction and logical order from a direct, intuitive grasp of the material, and hold that intuition matters to researchers and to anyone wanting to appreciate geometry. Topics range from the Leibniz series for pi, crystallographic groups and the regular polyhedra to sphere packing and Kepler's problem, projective configurations, non-Euclidean geometry and curvature, linkages, the Euler characteristic as a way of sorting manifolds, and the four color theorem. The English edition appeared in 1952.

Paul Graham listed it among the highly recommended books in his essay Undergraduation.