The Irrationals
A Story of the Numbers You Can't Count On
(Sprache: Englisch)
Fascinating and illuminating, this is a book for everyone who loves mathematics and the history behind it.
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Fascinating and illuminating, this is a book for everyone who loves mathematics and the history behind it.
Klappentext zu „The Irrationals “
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.
Inhaltsverzeichnis zu „The Irrationals “
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
Autoren-Porträt von Julian Havil
Julian Havil ist Master am renommierten Winchester-College in Südengland, wo er seit mehr als dreißig Jahren Mathematikunterricht gibt.
Bibliographische Angaben
- Autor: Julian Havil
- 2012, 312 Seiten, 100 Abbildungen, Maße: 16,5 x 3,2 cm, Gebunden, Englisch
- Verlag: Princeton University Press
- ISBN-10: 0691143420
- ISBN-13: 9780691143422
Sprache:
Englisch
Rezension zu „The Irrationals “
"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
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