The Enjoyment of Math

What is so special about the number 30? How many colors are needed to color a map? Do the prime numbers go on forever? Are there more whole numbers than even numbers? These and other mathematical puzzles are explored in this delightful book by two eminent mathematicians. Requiring no more background than plane geometry and elementary algebra, this book leads the reader into some of the most fundamental ideas of mathematics, the ideas that make the subject exciting and interesting. Explaining clearly how each problem has arisen and, in some cases, resolved, Hans Rademacher and Otto Toeplitz's deep curiosity for the subject and their outstanding pedagogical talents shine through.

Hans Rademacher was an Affiliate of Rockefeller University and Professor Emeritus of Mathematics at the University of Pennsylvania before his death in 1969 Otto Toeplitz was Professor of Mathematics in Kiel and Bonn

Preface	p. v
Introduction	p. 5
The Sequence of Prime Numbers	p. 9
Traversing Nets of Curves	p. 13
Some Maximum Problems	p. 17
Incommensurable Segments and Irrational Numbers	p. 22
A Minimum Property of the Pedal Triangle	p. 27
A Second Proof of the Same Minimum Property	p. 30
The Theory of Sets	p. 34
Some Combinatorial Problems	p. 43
On Waring's Problem	p. 52
On Closed Self-Intersecting Curves	p. 61
Is the Factorization of a Number into Prime Factors Unique?	p. 66
The Four-Color Problem	p. 73
The Regular Polyhedrons	p. 82
Pythagorean Numbers and Fermat's Theorem	p. 88
The Theorem of the Arithmetic and Geometric Means	p. 95
The Spanning Circle of a Finite Set of Points	p. 103
Approximating Irrational Numbers by Means of Rational Numbers	p. 111
Producing Rectilinear Motion by Means of Linkages	p. 119
Perfect Numbers	p. 129
Euler's Proof of the Infinitude of the Prime Numbers	p. 135
Fundamental Principles of Maximum Problems	p. 139
The Figure of Greatest Area with a Given Perimeter	p. 142
Periodic Decimal Fractions	p. 147
A Characteristic Property of the Circle	p. 160
Curves of Constant Breadth	p. 163
The Indispensability of the Compass for the Constructions of Elementary Geometry	p. 177
A Property of the Number 30	p. 187
An Improved Inequality	p. 192
Notes and Remarks	p. 197
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The Enjoyment of Math

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