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The Enjoyment of Math
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Hans Rademacher
Language:
English
Published/Copyright:
1967
About this book
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.
Author / Editor information
Hans Rademacher was an Affiliate of Rockefeller University and Professor Emeritus of Mathematics in the University of Pennsylvania before his death in 1969. Otto Toeplitz was Professor of Mathematics in Kiel and Bonn.
Reviews
A thoroughly enjoyable sampler of fascinating mathematical problems and their solutions.
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.
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Frontmatter
i -
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Preface
v -
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CONTENTS
1 -
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Introduction
5 -
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1. The Sequence of Prime Numbers
9 -
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2. Traversing Nets of Curves
13 -
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3. Some Maximum Problems
17 -
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4. Incommensurable Segments and Irrational Numbers
22 -
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5. A Minimum Property of the Pedal Triangle
27 -
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6. A Second Proof of the Same Minimum Property
30 -
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7. The Theory of Sets
34 -
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8. Some Combinatorial Problems
43 -
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9. On Waring's Problem
52 -
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10. On Closed Self-Intersecting Curves
61 -
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11. Is the Factorization of a Number into Prime Factors Unique?
66 -
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12. The Four-Color Problem
73 -
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13. The Regular Polyhedrons
82 -
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14. Pythagorean Numbers and Fermats Theorem
88 -
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15. The Theorem of the Arithmetic and Geometric Means
95 -
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16. The Spanning Circle of a Finite Set of Points
103 -
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17. Approximating Irrational Numbers by Means of Rational Numbers
111 -
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18. Producing Rectilinear Motion by Means of Linkages
119 -
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19. Perfect Numbers
129 -
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20. Euler's Proof of the Infinitude of the Prime Numbers
135 -
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21. Fundamental Principles of Maximum Problems
139 -
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22. The Figure of Greatest Area with à Given Perimeter
142 -
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23. Periodic Decimal Fractions
147 -
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24. A Characteristic Property of the Circle
160 -
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25. Curves of Constant Breadth
163 -
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26. The Indispensability of the Compass for the Constructions of Elementary Geometry
177 -
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27. A Property of the Number 30
187 -
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28. An Improved Inequality
192 -
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Notes and Remarks
197
Publishing information
Pages and Images/Illustrations in book
eBook published on:
June 5, 2018
eBook ISBN:
9780691186948
Pages and Images/Illustrations in book
eBook ISBN:
9780691186948
Keywords for this book
Theorem; Natural number; Remainder; Arc (geometry); Coprime integers; Parity (mathematics); Line segment; Straightedge; Regular polygon; Rational number; Trivium; Fractional part; Central angle; Infinit (file system); Prime number; Geometry; Smoothness; Convex curve; Irrational number; Combination
Audience(s) for this book
Professional and scholarly;College/higher education;
