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HOWARD EVES
The Dolciani Mathematical Expositions NUMBER FIVE
GREAT MOMENTS IN MATHEMATICS (BEFORE 1650)
By HOWARD EVES
University of Maine
Published and distributed by
THE MATHEMATICAL ASSOCIATION OF AMERICA
© 1983 by
The Mathematical Association oj America (Incorporated)
Library oj Congress Catalog Card Number 80-81046
For the Dolciani M athematical t.xpositions Series: ISBN-0-88385-300-0 For the Paperbound edition of Volume 5: ISBN-0-88385-310-8 Printed in the United States oj America
Current printing (last digit): 10 9 8 7 6 5 4 3 2 1
The DOLCIANI MATHEMATICAL EXPOSITIONS series of the Mathe matical Association of America was established through a generous gift to the Association from Mary P. Dolciani, Professor of Mathematics at Hunter College of the City University of New York . In making the gift, Professor Dolciani, herself an exceptionally talented and successful expositor of mathematics, had the purpose of furthering the ideal of excellence in mathematical exposition. The Association, for its part, was delighted to accept the gracious gesture initiating the revolving fund for this series from one who has served the Asso ciation with distinction, both as a member of the Committee on Publications and as a member of the Board of Governors. It was with genuine pleasure that the Board chose to name the series in her honor. The books in the series are selected for their lucid expository style and stimUlating mathematical content. Typically, they contain an ample supply of exercises, many with accompanying solutions. They are intended to be sufficiently elementary for the undergraduate and even the mathematically inclined high-school student to understand and enjoy, but also to be in teresting and sometimes challenging to the more advanced mathematician.
The following DOLCIANI MATHEMATICAL EXPOSITIONS have been published. by Ross Honsberger
Volume 1:
MATHEMATICAL GEMS,
Volume 2:
MATHEMATICAL GEMS II,
Volume 3:
MATHEMATICAL MORSELS,
Volume 4:
MATHEMATICAL PLUMS,
Volume 5:
by Ross Honsberger by Ross Honsberger
edited by Ross Honsberger
GREAT MOMENTS IN MATHEMATICS
Eves Volume 6: Volume 7:
( BEFORE 1650),
MAXIMA AND MINIMA WITHOUT CALCULUS, GREAT MOMENTS IN MATHEMATICS
Eves
by Howard
by Ivan Niven
( AFTER 1650),
by Howard
A GRATEFUL ACKNOWLEDGMENT
I wish to express my sincerest thanks to Professor Ross Honsberger and Professors G. L. Alexanderson, J. Malkevitch, and K. R. Reb man, Chairman and Members of the Dolciani Subcommittee, for their careful and constructive reading of the original manuscript. Their criticisms and suggestions were invaluable. HOWARD EVES
Dedicated to Carroll V. Newsom, in friendship and gratitude
PREFACE
Many who were growing up in America during the period from
1928 to 1942 will recall the extreme pleasure they experienced
when they tuned in their radios to the NBC "Music Appreciation Hour." During those fourteen years an estimated five million school children and a large unknown number of just plain devotees listened each week to the beautifully modulated and hypnotic voice of Walter Damrosch, eminent musicologist and master popularizer of good music. Week after week the listeners auricularly drank in the "great moments in music," and, ever after, their lives were en riched by knowing something of the noble accomplishments of the world's famous composers. Some years later, while serving in the Mathematics Department of Oregon State College, it occurred to me that what Walter Dam rosch so magnificently did for music could perhaps also be done for mathematics. Why not, I