Hidden Harmonies

The Lives and Times of the Pythagorean Theorem

Robert Kaplan, Ellen Kaplan

• Publisher: Bloomsbury Press
• Year: 2011
• Topic: Mathematics
• eBook ISBN:
  9781608192915
• Subtopic: Teaching Mathematics
• Index: Mathematics

A squared plus b squared equals c squared. It
sounds simple, doesn't it? Yet this familiar expression is a gateway
into the riotous garden of mathematics, and sends us on a journey of
exploration in the company of two inspired guides, acclaimed authors
Robert and Ellen Kaplan. With wit, verve, and clarity, they trace the
life of the Pythagorean theorem, from ancient Babylon to the present,
visiting along the way Leonardo da Vinci, Albert Einstein, President
James Garfield, and the Freemasons-not to mention the elusive Pythagoras
himself, who almost certainly did not make the statement that bears his
name.
How can a theorem have more than one proof? Why does this one have
more than two hundred-or is it four thousand? The Pythagorean theorem
has even more applications than proofs: Ancient Egyptians used it for
surveying property lines, and today astronomers call on it to measure
the distance between stars. Its generalizations are stunning-the theorem
works even with shapes on the sides that aren't squares, and not just
in two dimensions, but any number you like, up to infinity. And perhaps
its most intriguing feature of all, this tidy expression opened the door
to the world of irrational numbers, an untidy discovery that deeply
troubled Pythagoras's disciples.
Like the authors' bestselling The Nothing That Is and Chances Are . . .-hailed as "erudite and witty," "magnificent," and "exhilarating"- Hidden Harmonies makes the excitement of mathematics palpable.

Table of contents

• Cover
• Title Page
• Dedication
• Epigraph
• Contents
• An Outlook on Insights
• Chapter One: The Mathematician as Demigod
• Chapter Two: Desert Virtuosi
• Chapter Three: Through the Veil
• Chapter Four: Rebuilding the Cosmos
• Chapter Five: Touching the Bronze Sky
• Chapter Six: Exuberant Life
• Chapter Seven: Number Emerges from Shape
• Chapter Eight: Living at the Limit
• Chapter Nine: The Deep Point of the Dream
• Chapter Ten: Magic Casements
• Afterword: Reaching Through—or Past—History?
• Acknowledgments
• Notes
• Footnotes
• Selected Bibliography
• A Note on the Authors
• By the Same Authors
• eCopyright