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The Enjoyment of Math : Princeton Science Library - Hans Rademacher

The Enjoyment of Math

Princeton Science Library

Paperback

Published: 1st November 1966
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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

Prefacep. v
Introductionp. 5
The Sequence of Prime Numbersp. 9
Traversing Nets of Curvesp. 13
Some Maximum Problemsp. 17
Incommensurable Segments and Irrational Numbersp. 22
A Minimum Property of the Pedal Trianglep. 27
A Second Proof of the Same Minimum Propertyp. 30
The Theory of Setsp. 34
Some Combinatorial Problemsp. 43
On Waring's Problemp. 52
On Closed Self-Intersecting Curvesp. 61
Is the Factorization of a Number into Prime Factors Unique?p. 66
The Four-Color Problemp. 73
The Regular Polyhedronsp. 82
Pythagorean Numbers and Fermat's Theoremp. 88
The Theorem of the Arithmetic and Geometric Meansp. 95
The Spanning Circle of a Finite Set of Pointsp. 103
Approximating Irrational Numbers by Means of Rational Numbersp. 111
Producing Rectilinear Motion by Means of Linkagesp. 119
Perfect Numbersp. 129
Euler's Proof of the Infinitude of the Prime Numbersp. 135
Fundamental Principles of Maximum Problemsp. 139
The Figure of Greatest Area with a Given Perimeterp. 142
Periodic Decimal Fractionsp. 147
A Characteristic Property of the Circlep. 160
Curves of Constant Breadthp. 163
The Indispensability of the Compass for the Constructions of Elementary Geometryp. 177
A Property of the Number 30p. 187
An Improved Inequalityp. 192
Notes and Remarksp. 197
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780691023519
ISBN-10: 0691023514
Series: Princeton Science Library
Audience: Tertiary; University or College
Format: Paperback
Language: English
Number Of Pages: 216
Published: 1st November 1966
Publisher: Princeton University Press
Country of Publication: US
Dimensions (cm): 20.32 x 13.34  x 1.91
Weight (kg): 0.23