Chapters in this book

1. Frontmatter i
2. Preface v
3. CONTENTS 1
4. Introduction 5
5. 1. The Sequence of Prime Numbers 9
6. 2. Traversing Nets of Curves 13
7. 3. Some Maximum Problems 17
8. 4. Incommensurable Segments and Irrational Numbers 22
9. 5. A Minimum Property of the Pedal Triangle 27
10. 6. A Second Proof of the Same Minimum Property 30
11. 7. The Theory of Sets 34
12. 8. Some Combinatorial Problems 43
13. 9. On Waring's Problem 52
14. 10. On Closed Self-Intersecting Curves 61
15. 11. Is the Factorization of a Number into Prime Factors Unique? 66
16. 12. The Four-Color Problem 73
17. 13. The Regular Polyhedrons 82
18. 14. Pythagorean Numbers and Fermats Theorem 88
19. 15. The Theorem of the Arithmetic and Geometric Means 95
20. 16. The Spanning Circle of a Finite Set of Points 103
21. 17. Approximating Irrational Numbers by Means of Rational Numbers 111
22. 18. Producing Rectilinear Motion by Means of Linkages 119
23. 19. Perfect Numbers 129
24. 20. Euler's Proof of the Infinitude of the Prime Numbers 135
25. 21. Fundamental Principles of Maximum Problems 139
26. 22. The Figure of Greatest Area with à Given Perimeter 142
27. 23. Periodic Decimal Fractions 147
28. 24. A Characteristic Property of the Circle 160
29. 25. Curves of Constant Breadth 163
30. 26. The Indispensability of the Compass for the Constructions of Elementary Geometry 177
31. 27. A Property of the Number 30 187
32. 28. An Improved Inequality 192
33. Notes and Remarks 197