The Enjoyment of Mathematics: Selections from Mathematics for the Amateur - ISBN:0486262421

The Enjoyment of Mathematics: Selections from Mathematics for the Amateur

Date: 08 May 2011, 00:24

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Requiring only a basic background in plane geometry and elementary algebra, this classic poses 28 problems that introduce the fundamental ideas that make mathematics truly exciting. "Excellent . . . a thoroughly enjoyable sampler of fascinating mathematical problems and their solutions"-Science Magazine.
This is a superb book, and the best way to first sample the delights of math for its own sake. Don't let the subtitle "Selections from Mathematics for the Amateur" turn you off. True, the math involved is elementary, not going beyond high school algebra and geometry. But the material won't be found in most textbooks, having been chosen with elegance and beauty, rather than utility, in mind (which isn't to say that it doesn't have its important uses). Even the professional mathematician who has already seen most of the contents will profit from studying the book's exemplary treatment of its topics. The authors are some of the best math expositors who have ever lived. Each idea in the book is developed admirably, and strikes the perfect balance between conciseness and lucidity. You probably can't do better in choosing an introduction to prime and perfect numbers, the four-color problem, regular polyhedra, Pythagorean triples, pedal triangles, periodic decimal fractions, Waring's problem, the number 30 (sic!), and many other fascinating intellectual tibdits.
At Dover's low price, this book is a great buy. Get it! If you have more mathematical knowledge, then I also recommend "Proofs from the Book" by Aigner, et al., which is written for mathematicians in a similar style.
CONTENTS
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
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