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This title in other editionsThe Irrationalsby Julian Havil
Synopses & ReviewsPublisher 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 twentyfirst century. Along the way, he explains why irrational numbers are surprisingly difficult to defineand 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 twentyfirst century. Along the way, he explains why irrational numbers are surprisingly difficult to defineand 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 AuthorJulian 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 ContentsAcknowledgments 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 What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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