Irrationals A story of the numbers you can't count on

Includes index

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
8. Continued fractions revisited
9. The question and problem of randomness
10. One question, three answers
11. Does irrationality?

Annotation 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.