The Irrationals

A Story of the Numbers You Can't Count On

Julian Havil (Autor)

Buch | Hardcover

312 Seiten

2012
Princeton University Press (Verlag)
978-0-691-14342-2 (ISBN)

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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. This book tells the story of irrational numbers and the mathematicians who have tackled their challenges, from antiquity onwards.

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

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.

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 Apery 286 Appendix E Equivalence Relations 289 Appendix F The Mean Value Theorem 294 Index 295

Erscheint lt. Verlag	22.7.2012
Zusatzinfo	100 line illus.
Verlagsort	New Jersey
Sprache	englisch
Maße	152 x 235 mm
Gewicht	567 g
Themenwelt	Sachbuch/Ratgeber ► Natur / Technik
	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
	Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik
	Mathematik / Informatik ► Mathematik ► Mathematische Spiele und Unterhaltung
ISBN-10	0-691-14342-0 / 0691143420
ISBN-13	978-0-691-14342-2 / 9780691143422
Zustand	Neuware