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The Irrationals

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Synopses & Reviews

Publisher Comments:

The ancient Greeks discovered them, but it wasn't until the nineteenth century that irrational numbers were properly understood and rigorously defined, and even today not all their mysteries have been revealed. In The Irrationals, the first popular and comprehensive book on the subject, Julian Havil tells the story of irrational numbers and the mathematicians who have tackled their challenges, from antiquity to the twenty-first century. Along the way, he explains why irrational numbers are surprisingly difficult to define--and why so many questions still surround them.

That definition seems so simple: they are numbers that cannot be expressed as a ratio of two integers, or that have decimal expansions that are neither infinite nor recurring. But, as The Irrationals shows, these are the real "complex" numbers, and they have an equally complex and intriguing history, from Euclid's famous proof that the square root of 2 is irrational to Roger Apéry's proof of the irrationality of a number called Zeta(3), one of the greatest results of the twentieth century. In between, Havil explains other important results, such as the irrationality of e and pi. He also discusses the distinction between "ordinary" irrationals and transcendentals, as well as the appealing question of whether the decimal expansion of irrationals is "random".

Fascinating and illuminating, this is a book for everyone who loves math and the history behind it.

Synopsis:

"Readers will be swept away by Havil's command of the subject and his wonderful writing style. The Irrationals is a lot of fun."--Robert Gross, coauthor of Fearless Symmetry: Exposing the Hidden Patterns of Numbers and Elliptic Tales: Curves, Counting, and Number Theory

Synopsis:

The ancient Greeks discovered them, but it wasn't until the nineteenth century that irrational numbers were properly understood and rigorously defined, and even today not all their mysteries have been revealed. In The Irrationals, the first popular and comprehensive book on the subject, Julian Havil tells the story of irrational numbers and the mathematicians who have tackled their challenges, from antiquity to the twenty-first century. Along the way, he explains why irrational numbers are surprisingly difficult to define--and why so many questions still surround them.

That definition seems so simple: they are numbers that cannot be expressed as a ratio of two integers, or that have decimal expansions that are neither infinite nor recurring. But, as The Irrationals shows, these are the real "complex" numbers, and they have an equally complex and intriguing history, from Euclid's famous proof that the square root of 2 is irrational to Roger Apéry's proof of the irrationality of a number called Zeta(3), one of the greatest results of the twentieth century. In between, Havil explains other important results, such as the irrationality of e and pi. He also discusses the distinction between "ordinary" irrationals and transcendentals, as well as the appealing question of whether the decimal expansion of irrationals is "random".

Fascinating and illuminating, this is a book for everyone who loves math and the history behind it.

About the Author

Julian Havil is the author of "Gamma: Exploring Euler's Constant", "Nonplussed!: Mathematical Proof of Implausible Ideas", "Impossible?: Surprising Solutions to Counterintuitive Conundrums", and "John Napier: Life, Logarithms, and Legacy" (all Princeton). He is a retired former master at Winchester College, England, where he taught mathematics for more than three decades.

Table of Contents

Acknowledgments ix

Introduction 1

Chapter One Greek Beginnings 9

Chapter Two The Route to Germany 52

Chapter Three Two New Irrationals 92

Chapter Four Irrationals, Old and New 109

Chapter Five A Very Special Irrational 137

Chapter Six From the Rational to the Transcendental 154

Chapter Seven Transcendentals 182

Chapter Eight Continued Fractions Revisited 211

Chapter Nine The Question and Problem of Randomness 225

Chapter Ten One Question, Three Answers 235

Chapter Eleven Does Irrationality Matter? 252

Appendix A The Spiral of Theodorus 272

Appendix B Rational Parameterizations of the Circle 278

Appendix C Two Properties of Continued Fractions 281

Appendix D Finding the Tomb of Roger Apéry 286

Appendix E Equivalence Relations 289

Appendix F The Mean Value Theorem 294

Index 295

Product Details

ISBN:
9780691143422
Author:
Havil, Julian
Publisher:
Princeton University Press
Subject:
History
Subject:
Mathematics
Subject:
Physics
Subject:
History of Science and Medicine, Philosophy of Science
Subject:
Mathematics -- History.
Publication Date:
20120731
Binding:
HARDCOVER
Language:
English
Illustrations:
100 line illus.
Pages:
312
Dimensions:
9 x 6 in

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Related Subjects


» Reference » Science Reference » General
» Science and Mathematics » Mathematics » Foundations and Logic
» Science and Mathematics » Mathematics » History
» Science and Mathematics » Mathematics » Introduction
» Science and Mathematics » Mathematics » Number Theory
» Science and Mathematics » Physics » General

The Irrationals New Hardcover
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$29.95 In Stock
Product details 312 pages Princeton University Press - English 9780691143422 Reviews:
"Synopsis" by , "Readers will be swept away by Havil's command of the subject and his wonderful writing style. The Irrationals is a lot of fun."--Robert Gross, coauthor of Fearless Symmetry: Exposing the Hidden Patterns of Numbers and Elliptic Tales: Curves, Counting, and Number Theory
"Synopsis" by , The ancient Greeks discovered them, but it wasn't until the nineteenth century that irrational numbers were properly understood and rigorously defined, and even today not all their mysteries have been revealed. In The Irrationals, the first popular and comprehensive book on the subject, Julian Havil tells the story of irrational numbers and the mathematicians who have tackled their challenges, from antiquity to the twenty-first century. Along the way, he explains why irrational numbers are surprisingly difficult to define--and why so many questions still surround them.

That definition seems so simple: they are numbers that cannot be expressed as a ratio of two integers, or that have decimal expansions that are neither infinite nor recurring. But, as The Irrationals shows, these are the real "complex" numbers, and they have an equally complex and intriguing history, from Euclid's famous proof that the square root of 2 is irrational to Roger Apéry's proof of the irrationality of a number called Zeta(3), one of the greatest results of the twentieth century. In between, Havil explains other important results, such as the irrationality of e and pi. He also discusses the distinction between "ordinary" irrationals and transcendentals, as well as the appealing question of whether the decimal expansion of irrationals is "random".

Fascinating and illuminating, this is a book for everyone who loves math and the history behind it.

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