The enjoyment of mathematics : selections from mathematics for the amateur / by Hanz Rademacher and Otto Toeplitz ; translated by Herbert Zuckerman.

Format:

Book

Author/Creator:

Rademacher, Hanz, author.

Toeplitz, Otto, 1881-1940, author.

Contributor:

Zuckerman, Herbert, translator.

Series:

Princeton Legacy Library

Princeton Legacy Library ; 1970

Language:

English

Subjects (All):

Mathematical recreations.

Physical Description:

1 online resource (214 p.)

Place of Publication:

Princeton, New Jersey : Princeton University Press, 1957.

Language Note:

English

Summary:

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.Originally published in 1957.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Contents:

Frontmatter

Preface

Contents

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 online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

Description based on print version record.

"A translation from Von Zahlen und Figuren ... Chapters 15 and 28 by Herbert Zuckerman have been added to the English language edition."

Includes bibliographical references.

ISBN:

0-691-62676-6

1-4008-7608-7

OCLC:

945185872