文档介绍：To Alina and to Our Mothers
Titu Andreescu
Razvan˘ Gelca
Mathematical
Olympiad
Challenges
SECOND EDITION
Foreword by Mark Saul
Birkhäuser
Boston • Basel • Berlin
Titu Andreescu R
zvan Gelca
University of Texas at Dallas Texas Tech University
School of Natural Sciences Department of Mathematics
and Mathematics and Statistics
Richardson, TX 75080 Lubbock, TX 79409
USA USA
titu.******@ rgelca@
ISBN: 978-0-8176-4528-1 e-ISBN: 978-0-8176-4611-0
DOI: -0-8176-4611-0
Mathematics Subject Classification (2000): 00A05, 00A07, 05-XX, 11-XX, 51XX
© Birkhäuser Boston, a part of Springer Science+Business Media, LLC, Second Edition 2009
© Birkhäuser Boston, First Edition 2000
All rights reserved. This work may not be translated or copied in whole or in part without the written
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Printed on acid-free paper
Contents
Foreword xi
Preface to the Second Edition xiii
Preface to the First Edition xv
IProblems 1
1 Geometry and Trigonometry 3
................... 4
.......................... 6
............................. 10
Dissections of Polygonal Surfaces . . . ................ 15
Regular Polygons . ........................... 20
............. 25