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A Note on the Authors
ROBERT AND ELLEN KAPLAN have taught courses on subjects ranging from Sanskrit to Gödel’s Theorem, to students ranging in age from four to seventy. They are the authors of The Nothing That Is: A Natural History of Zero, The Art of the Infinite: The Pleasures of Mathematics, and Out of the Labyrinth: Setting Mathematics Free. Ellen Kaplan also coauthored with their son Michael Kaplan Chances Are . . .: Adventures in Probability and Bozo Sapiens: Why to Err is Human.
They founded the Math Circle in 1994 at Harvard and Northeastern Universities, and have taught thousands of students on both sides of the Atlantic and the Pacific.
By the Same Authors
The Nothing That Is: A Natural History of Zero
The Art of the Infinite: The Pleasures of Mathematics
Out of the Labyrinth: Setting Mathematics Free
Chances Are . . . Adventures in Probability
(Ellen Kaplan with Michael Kaplan)
Bozo Sapiens: Why to Err Is Human
(Ellen Kaplan with Michael Kaplan)
Copyright © 2011 by Robert and Ellen Kaplan
All rights reserved.
You may not copy, distribute, transmit, reproduce or otherwise make available this publication (or any part of it) in any form, or by any means (including without limitation electronic, digital, optical, mechanical, photocopying, printing, recording or otherwise), without the prior written permission of the publisher. Any person who does any unauthorized act in relation to this publication may be liable to criminal prosecution and civil claims for damages.
Published by Bloomsbury USA, New York
LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA
Kaplan, Robert, 1933-
Hidden harmonies : the lives and times of the Pythagorean theorem / Robert and Ellen Kaplan.- 1st U.S. ed.
p. cm.
Includes bibliographical references.
eISBN: 978-1-6081-9291-5
1. Pythagorean theorem-History. 2. Mathematics-History.
I. Kaplan, Ellen, 1936-II. Title.
QA460.P8K37 2010
516.22-dc22
2010019959
First published by Bloomsbury Press in 2011
This electronic edition published in 2013
www.bloomsburypress.com