The Irrationals : : A Story of the Numbers You Can't Count On / / / Julian Havil.

• VerfasserIn: Havil, Julian,
• Author: Havil, Julian,; Granville, Andrew,
• MitwirkendeR: Granville, Andrew,
• Place / Publishing House: Princeton, NJ : : : Princeton University Press, , [2023]; ©2012
• Year of Publication: 2023
• Language: English
• Series: Princeton Science Library ; ; 134
• Physical Description: 1 online resource (320 p.) :; 100 b/w illus.

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

Frontmatter -- Contents -- Foreword to the Princeton Science Library Edition -- Acknowledgments -- Introduction -- 1. Greek Beginnings -- 2. The Route to Germany -- 3. Two New Irrationals -- 4. Irrationals, Old and New -- 5. A Very Special Irrational -- 6. From the Rational to the Transcendental -- 7. Transcendentals If -- 8. Continued Fractions Revisited -- 9. The Question and Problem of Randomness -- 10. One Question, Three Answers -- 11. 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