Numbers: Histories, Mysteries, Theories

Numbers: Histories, Mysteries, Theories

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Overview

Posing the question "What exactly is a number?" a distinguished German mathematician presents this intriguing and accessible survey. Albrecht Beutelspacher ― founder of the renowned interactive mathematics museum, Mathematikum ― characterizes the wealth of experiences that numbers have to offer. In addition, he considers the many things that can be described by numbers and discusses which numbers possess special fascinations and pose lasting mysteries.
Starting with natural numbers, the book examines representations of numbers, rational and irrational numbers, transcendental numbers, and imaginary and complex numbers. Readers will explore the history of numbers from Pythagoras to Fermat and discover such practical applications as cryptography and barcodes. A thoughtful and enlightening introduction to the past, present, and future of numbers, this volume will captivate mathematicians and nonmathematicians alike.


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Product Details

ISBN-13: 9780486803487
Publisher: Dover Publications
Publication date: 01/14/2016
Series: Aurora: Dover Modern Math Originals Series
Pages: 112
Sales rank: 379,946
Product dimensions: 5.90(w) x 8.80(h) x 0.30(d)

About the Author



German mathematician Albrecht Beutelspacher is well known in his native country as a writer of books on popular science and recreational mathematics. He is also the founder of Germany's first math museum, the Mathematikum.

Table of Contents

Preface vii

1 Natural numbers 1

1.1 Counting 1

1.2 Properties of numbers 3

1.3 Magic squares 7

1.4 Prime numbers 8

1.5 From Pythagoras to Fermat 13

1.6 What are natural numbers? 16

1.7 Applications: Cryptography 19

2 Representations of numbers 23

2.1 How were numbers written in former times? 23

2.2 The abacus and counting board 26

2.3 The decimal system 31

2.4 Divisibility rules 33

2.5 Binary numbers 36

2.6 Applications: Barcodes 38

3 Rational and irrational 41

3.1 Fractions 41

3.2 Ratios 44

3.3 Rational numbers 48

3.4 Irrational numbers: The first crisis 52

3.5 Decimal numbers 57

4 Transcendental numbers 61

4.1 The most mysterious number 61

4.2 Limits 64

4.3 How many transcendental numbers are there? 70

5 Imaginary and complex 75

5.1 Linear equations 76

5.2 Quadratic equations 77

5.3 The drama of the cubic equation 80

5.4 The tragedy of the quintic equation 82

5.5 Every equation can be solved! 84

Additional Notes 89

Bibliography 99

Index 101

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