The enjoyment of math / Hans Rademacher and Otto Toeplitz ; with a new foreword by Alex Kontorovich.

Format:

Book

Author/Creator:

Rademacher, Hans, 1892-1969, author.

Toeplitz, Otto, 1881-1940, author.

Contributor:

Kontorovich, Alex, writer of foreword.

Series:

Princeton science library.

Princeton science library

Language:

English

Subjects (All):

Mathematical recreations.

Genre:

Popular works.

Physical Description:

1 online resource (vii, 197 pages) : illustrations.

Place of Publication:

Princeton, New Jersey ; Oxford : Princeton University Press, 2023.

Summary:

The classic book that shares the enjoyment of mathematics with readers of all skill levelsWhat 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.

Contents:

Frontmatter

CONTENTS

Foreword

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

Notes:

Description based on print version record.

ISBN:

9780691241531

0691241538

OCLC:

1345584902