The enjoyment of math

Frontmatter CONTENTS Foreword Preface Introduction 1. The Sequence of Prime Numbers 2. Traversing Nets of Curves 3. Some Maximum Problems 4. Incommensurable Segments and Irrational Numbers 5. A Minimum Property of the Pedal Triangle 6. A Second Proof of the Same Minimum Property 7. The Theory of Sets 8. Some Combinatorial Problems 9. On Waring's Problem 10. On Closed Self-Intersecting Curves 11. Is the Factorization of a Number into Prime Factors Unique? 12. The Four-Color Problem 13. The Regular Polyhedrons 14. Pythagorean Numbers and Fermat's Theorem 15. The Theorem of the Arithmetic and Geometric Means 16. The Spanning Circle of a Finite Set of Points 17. Approximating Irrational Numbers by Means of Rational Numbers 18. Producing Rectilinear Motion by Means of Linkages 19. Perfect Numbers 20. Euler's Proof of the Infinitude of the Prime Numbers 21. Fundamental Principles of Maximum Problems 22. The Figure of Greatest Area with a Given Perimeter 23. Periodic Decimal Fractions 24. A Characteristic Property of the Circle 25. Curves of Constant Breadth 26. The Indispensability of the Compass for the Constructions of Elementary Geometry 27. A Property of the Number 30 28. An Improved Inequality Notes and Remarks

The classic book that shares the enjoyment of mathematics with readers of all skill levelsWhat is so special about the number 30? Do the prime numbers go on forever? Are there more whole numbers than even numbers? The Enjoyment of Math explores these and other captivating problems and puzzles, introducing readers to some of the most fundamental ideas in mathematics. Written by two eminent mathematicians and requiring only a background in plane geometry and elementary algebra, this delightful book covers topics such as the theory of sets, the four-color problem, regular polyhedrons, Euler's proof of the infinitude of prime numbers, and curves of constant breadth. Along the way, it discusses the history behind the problems, carefully explaining how each has arisen and, in some cases, how to resolve it. With an incisive foreword by Alex Kontorovich, this Princeton Science Library edition shares the enjoyment of math with a new generation of readers.