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.
Author(s): Hans Rademacher (author), Otto Toeplitz (author), Herbert Zuckerman (Translator)
Series: Princeton Science Library, 138
Edition: 1
Publisher: Princeton University Press
Year: 2023
Language: English
Commentary: Translation from: http://anonym.to/?https://doi.org/10.1007/978-3-662-36239-6 | pending LCC classification: http://anonym.to/?https://lccn.loc.gov/2022942877
Pages: 224
City: New Jersey, Oxford
Tags: Mathematik; Mathematics; Prime Numbers; Maximum Problems; Irrational Numbers; Sets Theory; Combinatorial Problems; Four-Color Problem; Pythagorean Numbers; Fermat's Theorem; Arithmetic Means; Geometric Means; Perfect Numbers; Euler's Proof; Number 30
Cover
Contents
Foreword by Alex Kontorovich
Preface
Introduction
1. The Sequence of Prime Numbers
2. Traversing Nets of Curves
3. Some Maximum Problems
4. Incommensurable Segments and Irrational Numbers
5. A Minimum Property of the Pedal Triangle
6. A Second Proof of the Same Minimum Property
7. The Theory of Sets
8. Some Combinatorial Problems
9. On Waring's Problem
10. On Closed Self-Intersecting Curves
11. Is the Factorization of a Number into Prime Factors Unique?
12. The Four-Color Problem
13. The Regular Polyhedrons
14. Pythagorean Numbers and Fermat's Theorem
15. The Theorem of the Arithmetic and Geometric Means
16. The Spanning Circle of a Finite Set of Points
17. Approximating Irrational Numbers by Means of Rational Numbers
18. Producing Rectilinear Motion by Means of Linkages
19. Perfect Numbers
20. Euler's Proof of the Infinitude of the Prime Numbers
21. Fundamental Principles of Maximum Problems
22. The Figure of Greatest Area with a Given Perimeter
23. Periodic Decimal Fractions
24. A Characteristic Property of the Circle
25. Curves of Constant Breadth
26. The Indispensability of the Compass for the Constructions of Elementary Geometry
27. A Property of the Number 30
28. An Improved Inequality
Notes and Remarks
