Geometric Inequalities Methods of Proving
This unique collection of new and classical problems provides full coverage of geometric inequalities. Many of the 1,000 exercises are presented with detailed author-prepared-solutions, developing creativity and an arsenal of new approaches for solving ma
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Hayk Sedrakyan Nairi Sedrakyan
Geometric Inequalities Methods of Proving
Problem Books in Mathematics Series Editor: Peter Winkler Department of Mathematics Dartmouth College Hanover, NH 03755 USA
More information about this series at http://www.springer.com/series/714
Hayk Sedrakyan • Nairi Sedrakyan
Geometric Inequalities Methods of Proving B r1 r3 r2 A
r1 + r 2 > r 3
C
Hayk Sedrakyan University Pierre and Marie Curie Paris, France
Nairi Sedrakyan Yerevan, Armenia
ISSN 0941-3502 ISSN 2197-8506 (electronic) Problem Books in Mathematics ISBN 978-3-319-55079-4 ISBN 978-3-319-55080-0 (eBook) DOI 10.1007/978-3-319-55080-0 Library of Congress Control Number: 2017937367 Mathematics Subject Classification (2010): 00A07 © Springer International Publishing AG 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
To Margarita, a wonderful wife and a loving mother To Ani, a wonderful daughter and a loving sister
Preface
Geometric inequalities are one of the most interesting sections of elementary mathematics and have a wide range of applications in geometry and the other fields of mathematics, such as algebra and trigonometry. To prove geometric inequalities one often has to use, besides the geometric reasoning, algebraic transformations, trigonometric relations and inequalities, calculus and mathematical analysis. This book is the third book of the authors about inequalities. The first two books were dedicated to algebraic inequalities and were published in 2015 in South Korea. All these books reflect long years of experience of the authors in teaching. Most of the problems were created or proved by the authors during those classes. Th
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