The Irrationals

A Story of the Numbers You Can't Count On

Nonfiction, Science & Nature, Mathematics, Number Theory, History, Science
Cover of the book The Irrationals by Julian Havil, Princeton University Press
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Julian Havil ISBN: 9781400841707
Publisher: Princeton University Press Publication: July 22, 2012
Imprint: Princeton University Press Language: English
Author: Julian Havil
ISBN: 9781400841707
Publisher: Princeton University Press
Publication: July 22, 2012
Imprint: Princeton University Press
Language: English

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. But, as The Irrationals shows, these are the real "complex" numbers, and they have an equally complex and intriguing history, from Euclid's famous proof that the square root of 2 is irrational to Roger Apéry's proof of the irrationality of a number called Zeta(3), one of the greatest results of the twentieth century. In between, Havil explains other important results, such as the irrationality of e and pi. He also discusses the distinction between "ordinary" irrationals and transcendentals, as well as the appealing question of whether the decimal expansion of irrationals is "random".

Fascinating and illuminating, this is a book for everyone who loves math and the history behind it.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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. But, as The Irrationals shows, these are the real "complex" numbers, and they have an equally complex and intriguing history, from Euclid's famous proof that the square root of 2 is irrational to Roger Apéry's proof of the irrationality of a number called Zeta(3), one of the greatest results of the twentieth century. In between, Havil explains other important results, such as the irrationality of e and pi. He also discusses the distinction between "ordinary" irrationals and transcendentals, as well as the appealing question of whether the decimal expansion of irrationals is "random".

Fascinating and illuminating, this is a book for everyone who loves math and the history behind it.

More books from Princeton University Press

Cover of the book Collected Works of C.G. Jung, Volume 11 by Julian Havil
Cover of the book What We Owe Iraq by Julian Havil
Cover of the book The Makings of Indonesian Islam by Julian Havil
Cover of the book Climbing the Charts by Julian Havil
Cover of the book Topics in Quaternion Linear Algebra by Julian Havil
Cover of the book Modern Anti-windup Synthesis by Julian Havil
Cover of the book Kierkegaard's Writings, VIII: Concept of Anxiety: A Simple Psychologically Orienting Deliberation on the Dogmatic Issue of Hereditary Sin by Julian Havil
Cover of the book Knocking on the Door by Julian Havil
Cover of the book The Pocket Instructor: Literature by Julian Havil
Cover of the book The End of the West: The Once and Future Europe by Julian Havil
Cover of the book Strangers to the Constitution by Julian Havil
Cover of the book Trustworthy Men by Julian Havil
Cover of the book The Theory of Ecological Communities (MPB-57) by Julian Havil
Cover of the book The Constitution of Ancient China by Julian Havil
Cover of the book Interaction Ritual Chains by Julian Havil
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy