Date: 2010

Page count: 321 pages

Format: B/5

ISBN: 978-963-2790-29-9

Category: from German

Original price: 2900 Ft

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.

"A thoroughly enjoyable sampler of fascinating mathematical problems
and their solutions."--*Science*

"Each chapter is a gem of mathematical exposition.... [The book] will
not only stretch the imagination of the amateur, but it will also give pleasure
to the sophisticated mathematician."--*American Mathematical Monthly*

** TABLE OF CONTENTS:**

Preface v

Introduction 5

1. The Sequence of Prime Numbers 9

2. Traversing Nets of Curves 13

3. Some Maximum Problems 17

4. Incommensurable Segments and Irrational Numbers 22

5. A Minimum Property of the Pedal Triangle 27

6. A Second Proof of the Same Minimum Property 30

7. The Theory of Sets 34

8. Some Combinatorial Problems 43

9. On Waring's Problem 52

10. On Closed Self-Intersecting Curves 61

11. Is the Factorization of a Number into Prime Factors Unique?66

12. The Four-Color Problem 73

13. The Regular Polyhedrons 82

14. Pythagorean Numbers and Fermat's Theorem 88

15. The Theorem of the Arithmetic and Geometric Means 95

16. The Spanning Circle of a Finite Set of Points 103

17. Approximating Irrational Numbers by Means of Rational Numbers ill

18. Producing Rectilinear Motion by Means of Linkages 119

19. Perfect Numbers 129

20. Euler's Proof of the Infinitude of the Prime Numbers 135

21. Fundamental Principles of Maximum Problems 139

22. The Figure of Greatest Area with a Given Perimeter 142

23. Periodic Decimal Fractions 147

24. A Characteristic Property of the Circle 160

25. Curves of Constant Breadth 163

26. The Indispensability of the Compass for the Constructions of Elementary
Geometry 177

27. A Property of the Number 30 187

28. An Improved Inequality 192

Notes and Remarks 197