100Great problems of elementary mathematics

100 Great Problems of Elementary Mathematics
THEIR HISTORY AND SOLUTION

BY HEINRICH DORRIE

TRANSLATED BY DAVID ANTIN

NEW YORK DOVER PUBLICATIONS, INC.

Copyright © 1965 by Dover Publications. Inc.: originally published in German under the title of Triumph der Mathematik, © 1958 by PhysicaYerlag. WUrzburg. All rights reserved under Pan American and International Copyright Conventions.

Published in Canada by General Publishing Company. Ltd., 30 Lesmill Road. Don Mills. Toronto, Ontario. Published in the United Kingdom by Constable and Company, Ltd .• 10 Orange Street, London WC 2.

This Dover edition. first published in 1965. is a new translation of the unabridged text of the fifth edition of the work published by the Physica-Yerlag. Wiirzburg, Germany. in 1958 under the title Triumph der Mathematik: Hundert beruhmte Probleme aw %wei Jahrtawenden mathematischer Kultur. This authorized translation is published by special arrangement with the German-language publishers. Physica-Yerlag. Wiirzburg.

Standard Book Number: 486-61348-8 Library of Congress Catalog Card Number:65-140JO

Manufactured in the United States of America Dover Publications, Inc. 180 Yarick Street New York. N.Y. 10014

Preface
A book collecting the celebrated problems of elementary mathematics that would commemorate their origin and, above all, present their solutions briefly, clearly, and comprehensibly has long seemed a necessary and attractive task to the author. The restriction to problems of elementary mathematics was considered advisable in view of those readers who have neither the time nor the opportunity to acquaint themselves in any detail with higher mathematics. Nevertheless, in spite of this limitation a colorful and compelling picture has emerged, one that gives an idea of the amazing variety of mathematical methods and one that will-I hope-enchant many who are interested in mathematics and who take pleasure in characteristic mathematical thought processes. In