ジュリアン・ハヴィル『無理数の話 √2の発見から超越数の謎まで』（原書） The Irrationals : A Story of the Numbers You Can't Count on

Havil, Julian

Princeton Univ Pr（2012/07発売）

• 製本 Hardcover:ハードカバー版／ページ数 298 p.／サイズ 100 line illus.
• 言語 ENG
• 商品コード 9780691143422
• DDC分類 512.73

基本説明

邦訳：2012年10月・青土社。The first popular history of Irrational Numbers and their discoverers, from ancient Greece to the twenty-first century.

Full Description

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.

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