Buch, Englisch, 320 Seiten, Format (B × H): 164 mm x 249 mm, Gewicht: 594 g
ISBN: 978-0-691-14342-2
Verlag: Princeton University Press
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.
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
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 Ap?ry 286
Appendix E Equivalence Relations 289
Appendix F The Mean Value Theorem 294
Index 295
