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The classic book that shares the enjoyment of mathematics with readers of all skill levels.
What 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.
Foreword by Alex Kontorovich (2022).
Preface (H. Rademacher, 1956).
Introduction.
The Sequence of Prime Numbers.
Traversing Nets of Curves.
Some Maximum Problems.
Incommensurable Segments and Irrational Numbers.
A Minimum Property of the Pedal Triangle.
A Second Proof of the Same Minimum Property.
The Theory of Sets.
Some Combinatorial Problems.
On Waring's Problem.
On Closed Self-Intersecting Curves.
Is the Factorization of a Number into Prime Factors Unique?
The Four-Color Problem.
The Regular Polyhedrons.
Pythagorean Numbers and Fermat's Theorem.
The Theorem of the Arithmetic and Geometric Means.
The Spanning Circle of a Finite Set of Points.
Approximating Irrational Numbers by Means of Rational Numbers.
Producing Rectilinear Motion by Means of Linkages.
Perfect Numbers.
Euler's Proof of the Infinitude of the Prime Numbers.
Fundamental Principles of Maximum Problems.
The Figure of Greatest Area with a Given Perimeter.
Periodic Decimal Fractions.
A Characteristic Property of the Circle.
Curves of Constant Breadth.
The Indispensability of the Compass for the Constructions of Elementary Geometry.
A Property of the Number 30.
An Improved Inequality.
Notes and Remarks