THE ENJOYMENT OF
MATHEMATICS
Hans Rademacher
Otto Toeplitz
CONTENTS
Preface
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 Ceometry
- A Property of the Number 30
- An Improved Inequality
Notes and Remarks
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