Hans Rademacher, Otto Toeplitz

The Enjoyment of Math (eBook, PDF)

• Format: PDF

Produktbeschreibung

The classic book that shares the enjoyment of mathematics with readers of all skill levels

What is so special about the number 30? Do the prime numbers go on forever? Are there more whole numbers than even numbers? The Enjoyment of Math explores these and other captivating problems and puzzles, introducing readers to some of the most fundamental ideas in mathematics. Written by two eminent mathematicians and requiring only a background in plane geometry and elementary algebra, this delightful book covers topics such as the theory of sets, the four-color problem, regular polyhedrons, Euler's proof of the infinitude of prime numbers, and curves of constant breadth. Along the way, it discusses the history behind the problems, carefully explaining how each has arisen and, in some cases, how to resolve it. With an incisive foreword by Alex Kontorovich, this Princeton Science Library edition shares the enjoyment of math with a new generation of readers.

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Produktdetails

• Verlag: University of Pittsburgh Press
• Erscheinungstermin: 24. Januar 2023
• Englisch
• ISBN-13: 9780691241531
• Artikelnr.: 63728136

Autorenporträt

Hans Rademacher (1892-1969) was professor emeritus of mathematics at the University of Pennsylvania. Otto Toeplitz (1881-1940) was a leading mathematician specializing in linear algebra and functional analysis. Alex Kontorovich is professor of mathematics at Rutgers University.

Inhaltsangabe

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

Rezensionen

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.