The Irrationals

A Story of the Numbers You Can't Count On

Julian Havil

• Publisher: Princeton University Press
• Year: 2023
• Topic: Mathematics
• Print ISBN:
  9780691247663
• Subtopic: History & Philosophy of Mathematics
• eBook ISBN:
  9780691247670
• Index: Mathematics

An entertaining and enlightening history of irrational numbers, from ancient Greece to the twenty-first century

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.

Table of contents

• Cover
• Contents
• Foreword to the Princeton Science Library Edition
• Acknowledgments
• Introduction
• Chapter One. Greek Beginnings
• Chapter Two. The Route to Germany
• Chapter Three. Two New Irrationals
• Chapter Four. Irrationals, Old and New
• Chapter Five. A Very Special Irrational
• Chapter Six. From the Rational to the Transcendental
• Chapter Seven. Transcendentals
• Chapter Eight. Continued Fractions Revisited
• Chapter Nine. The Question and Problem of Randomness
• Chapter Ten. One Question, Three Answers
• Chapter Eleven. Does Irrationality Matter
• Appendix A. The Spiral of Theodorus
• Appendix B. Rational Parameterizations of the Circle
• Appendix C. Two Properties of Continued Fractions
• Appendix D. Finding the Tomb of Roger Apéry
• Appendix E. Equivalence Relations
• Appendix F. The Mean Value Theorem
• Index