Chapters in this book

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