Geometry and the Imagination

GeoAndImagNovember’s Book of the Month is Geometry and the Imagination by Hilbert and Cohn-Vossen. First published in 1952.

The AMS website says: “This remarkable book has endured as a true masterpiece of mathematical exposition. … The book is overflowing with mathematical ideas, which are always explained clearly and elegantly, and above all, with penetrating insight. It is a joy to read, both for beginners and experienced mathematicians.
[It] is full of interesting facts, many of which you wish you had known before. … The book begins with examples of the simplest curves and surfaces, including thread constructions of certain quadrics and other surfaces. The chapter on regular systems of points leads to the crystallographic groups and the regular polyhedra in \mathbb{R}^3. …
One of the most remarkable chapters is “Projective Configurations”. … Hilbert and Cohn-Vossen give perhaps the most concise and lucid description of why a general geometer would care about projective geometry and why such an ostensibly plain setup is truly rich in structure and ideas. …
A particularly intriguing section … is Eleven Properties of the Sphere. Which eleven properties of such a ubiquitous mathematical object caught their discerning eye and why? … The book includes pictures of some of the models that are found in the Göttingen collection. Furthermore, the mysterious lines that mark these surfaces are finally explained! …”

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