Euler's Gem

How a simple equation reshaped mathematics

Leonhard Euler’s polyhedron formula describes the structure of many objects—from soccer balls and gemstones to Buckminster Fuller’s buildings and giant all-carbon molecules. Yet Euler’s theorem is so simple it can be explained to a child. From ancient Greek geometry to today’s cutting-edge research, Euler’s Gem celebrates the discovery of Euler’s beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. Using wonderful examples and numerous illustrations, David Richeson presents this mathematical idea’s many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map. Filled with a who’s who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem’s development, Euler’s Gem will fascinate every mathematics enthusiast. This paperback edition contains a new preface by the author.

“The author has achieved a remarkable feat, introducing a naïve reader to a rich history without compromising the insights and without leaving out a delicious detail. . . . An awe-inspiring experience.”—Choice

“This is an excellent book about a great man and a timeless formula.”—Charles Ashbacher, Journal of Recreational Mathematics

“It was a pleasure reading this book, and I recommend it to everyone who is not afraid of mathematical arguments and has ever wondered what this field of ‘rubbersheet geometry’ is about. You will not be disappointed.”—Jeanine Daems, Mathematical Intelligencer

“David Richeson’s Euler’s Gem does an outstanding job of explaining serious mathematics to a general audience. . . . The book succeeds at showing the reader a lot of attractive mathematics with a well-chosen level of technical detail.”—Jeremy L. Martin, Notices of the AMS