The Cult of Pythagoras Math and Myths

289 Pages·2012·3.19 MB·English

by  Alberto A. Martinez

The Cult of Pythagoras

THE CULT OF
PYTHAGOR AS
Math and Myths
ALBERTO A. MARTÍNEZ
University of Pittsburgh Press
Published by the University of Pittsburgh Press, Pittsburgh, Pa., 15260
Copyright © 2012, Alberto A. Martínez
All rights reserved
Manufactured in the United States of America
Printed on acid-free paper
First paperback edition 2013
10 9 8 7 6 5 4 3 2 1
Library of Congress Cataloging-in-Publication Data
Martinez, Alberto A.
The cult of Pythagoras : math and myths / Alberto A. Martinez.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-8229-4418-8 (hardcover : alk. paper)
1. Mathematics—History. 2. Geometry—History. I. Title.
QA21.M335 2012
910.938—dc23 2012022366>
From of old it has been the custom,
and not only in our time,
for vice to make war on virtue.
Thus Pythagoras, with three hundred others,
was burned to death.
—Cohort ad Græcos, ca. 150 CE

CONTENTS
List of Myths and Apparent Myths ix
Acknowledgments xiii
Introduction xvii
1. Triangle Sacriice to the Gods 1
2. An Irrational Murder at Sea 16
3. Ugly Old Socrates on Eternal Truth 29
4. The Death of Archimedes 43
5. Gauss, Galois, and the Golden Ratio 59
6. From Nothing to Ininity 82
7. Euler’s Imaginary Mistakes 101
8. The Four of Pythagoras 113
9. The War over the Ininitely Small 134
10. Impossible Triangles 156
11. Inventing Mathematics? 181
12. The Cult of Pythagoras 201
Notes 217
Illustration Sources and Credits 257
Index 259

LIST OF MYTHS AND APPARENT MYTHS
Did Pythagoras discover the hypotenuse theorem? 1
Was Pythagoras a mathematician? 2
Did Pythagoras prove the hypotenuse theorem? 8
Did Pythagoras believe that the world is made of numbers? 16
Did Pythagoras discover the theory of irrationals? 20
Was Hippasus murdered for revealing irrational numbers? 21
Did Hippasus discover irrationality in a pentagram? 21
Did Socrates value mathematics as an end in itself? 35
Did Archimedes solve the weight of a golden crown? 48
Did a soldier kill Archimedes for defending a diagram? 53
Did the bright boy Gauss add all numbers from 1 to 100? 59
Did Galois create group theory the night before dying by gunshot? 61
Did the Egyptians use the golden ratio in the Great Pyramid? 76
Did Pythagoras discover the golden ratio in a pentagram? 77
Is the golden ratio found in ancient architecture? 77
Do most people prefer the shape of golden rectangles? 78
Does the navel divide the body according to the golden section? 78
ix