Proofs from the Book

From the reviews of the first edition: "Anyone who enjoys the logic and reasoning of mathematics and has a strong undergraduate mathematics background should enjoy this book...I would imagine that few mathematicians have seen all these proofs. The combination of ideas in many of the proofs should delight mathematicians everywhere." - MAA ONLINE The (mathematical) heroes of this book are "perfect proofs": brilliant ideas, clever connections and wonderful observations that bring new insight and surprising perspectives on basic and challenging problems from number theory, geometry, analysis, combinatorics, and graph theory. Thirty beautiful examples are presented here. They are candidates for THE BOOK in which God records the perfect proofs - according to the late Paul Erdös, who suggested many of the topics in this collection. The result is a book which will be fun for everybody with an interest in mathematics, requiring only a very modest (undergraduate) mathematical background. For this revised and expanded second edition several chapters have been revised and expanded, and three new chapters have been added.