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The Enjoyment of Math
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Hans Rademacher
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Preface by:
Alex Kontorovich
Language:
English
Published/Copyright:
2023
About this book
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 / Editor information
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.
Reviews
“A thoroughly enjoyable sampler of fascinating mathematical problems and their solutions.”—Science
“Each chapter is a gem of mathematical exposition. . . . [The Enjoyment of Math] will not only stretch the imagination of the amateur, but it will also give pleasure to the sophisticated mathematician.”—American Mathematical Monthly
“Each chapter is a gem of mathematical exposition. . . . [The Enjoyment of Math] will not only stretch the imagination of the amateur, but it will also give pleasure to the sophisticated mathematician.”—American Mathematical Monthly
Topics
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Frontmatter
i -
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CONTENTS
v -
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Foreword
vii -
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Preface
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 Fermat's 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 a 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:
January 24, 2023
eBook ISBN:
9780691241531
Pages and Images/Illustrations in book
Main content:
216
Other:
123 b/w illus.
eBook ISBN:
9780691241531
Keywords for this book
Theorem; Natural number; Prime number; Summation; Divisor; Prime factor; Parity (mathematics); Mathematics; Coprime integers; Rhomboid; Perfect number; Circumference; Remainder; Factorization; Fourth power; Rectangle; Pedal triangle; Polyhedron; Regular polyhedron; Diameter; Parallelogram; Equilateral triangle; Pythagorean theorem; Line segment; Right triangle; Sign (mathematics); Geometry; Special case; Arbitrarily large; Fermat's Last Theorem; Rational number; Prime number theorem; Straightedge; Big O notation; Transfinite number; Irrational number; Right angle; Scientific notation; Hypotenuse; Bonse's inequality; Prime power; Non-Euclidean geometry; Metric space; Coefficient; Waring's problem; Integer factorization; Pure mathematics; Rhombus; Factorial; Euler's theorem; Intersection (set theory); Combination; Complete theory; Reuleaux triangle; Geometric series; Fractional part; Binomial theorem; Number theory; Computation; Euler's formula; Variable (mathematics); Power of 10; Fermat's theorem; Exterior (topology); Regular polygon; Logarithm; Long division; Mathematical induction; Arithmetic; Geometric mean
Audience(s) for this book
College/higher education;Professional and scholarly;
