The Irrationals: A Story of the Numbers You Can't Count On

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Princeton University Press, 22 de jul. 2012 - 312 pàgines

The first popular history of irrational numbers and their discoverers, 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.

 

Continguts

Introduction
1
Greek Beginnings
9
The Route to Germany
52
Two New Irrationals
92
Irrationals Old and New
109
A Very Special Irrational
137
From the Rational to the Transcendental
154
Transcendentals
182
One Question Three Answers
235
Does Irrationality Matter?
252
The Spiral of Theodorus
272
Rational Parameterizations of the Circle
278
Two Properties of Continued Fractions
281
Finding the Tomb of Roger Apéry
286
Equivalence Relations
289
The Mean Value Theorem
294

Continued Fractions Revisited
211
The Question and Problem of Randomness
225

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Sobre l'autor (2012)

Julian Havil is the author of Gamma: Exploring Euler's Constant, Nonplussed!: Mathematical Proof of Implausible Ideas, Impossible?: Surprising Solutions to Counterintuitive Conundrums, and John Napier: Life, Logarithms, and Legacy (all Princeton). He is a retired former master at Winchester College, England, where he taught mathematics for more than three decades.

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