© 2017

Geometric Inequalities

Methods of Proving


  • Contains more than 1,000 problems

  • Provides an easy-to-understand approach to train for mathematic olympiads

  • Promotes creativity for solving math problems while learning new approaches

  • Includes classical, well-known solutions combined with new problems


Part of the Problem Books in Mathematics book series (PBM)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Hayk Sedrakyan, Nairi Sedrakyan
    Pages 1-38
  3. Hayk Sedrakyan, Nairi Sedrakyan
    Pages 39-91
  4. Hayk Sedrakyan, Nairi Sedrakyan
    Pages 93-138
  5. Hayk Sedrakyan, Nairi Sedrakyan
    Pages 139-165
  6. Hayk Sedrakyan, Nairi Sedrakyan
    Pages 167-259
  7. Hayk Sedrakyan, Nairi Sedrakyan
    Pages 261-284
  8. Hayk Sedrakyan, Nairi Sedrakyan
    Pages 285-411
  9. Hayk Sedrakyan, Nairi Sedrakyan
    Pages 413-445
  10. Back Matter
    Pages 447-449

About this book


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 mathematical problems. This book can serve teachers, high-school students, and mathematical competitors. It may also be used as supplemental reading, providing readers with new and classical methods for proving geometric inequalities. 


Geometric Inequalities Mathematical Olympiad Problems Inequality Problems and Solutions Method of Projections Mathematical Competitions Textbook Vectors Inradius and Circumradius Trigonometry

Authors and affiliations

  1. 1.University Pierre and Marie CurieParisFrance
  2. 2.YerevanArmenia

About the authors

Hayk Sedrakyan is an IMO medal winner Professor of mathematics in Paris, France and a professional Math Olympiad Coach in Greater Boston area, Massachusetts, USA. He has defended his PhD thesis in mathematics in UPMC-Sorbonne University, Paris, France.

Nairi Sedrakyan is involved in national and international Olympiads of mathematics, having been the President of Armenian Mathematics Olympiads and IMO jury member. He is the author of one of the hardest problems ever proposed in the history of IMO.

Bibliographic information

  • Book Title Geometric Inequalities
  • Book Subtitle Methods of Proving
  • Authors Hayk Sedrakyan
    Nairi Sedrakyan
  • Series Title Problem Books in Mathematics
  • Series Abbreviated Title Problem Books Mathematics
  • DOI
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-319-55079-4
  • Softcover ISBN 978-3-319-85561-5
  • eBook ISBN 978-3-319-55080-0
  • Series ISSN 0941-3502
  • Series E-ISSN 2197-8506
  • Edition Number 1
  • Number of Pages XII, 452
  • Number of Illustrations 263 b/w illustrations, 5 illustrations in colour
  • Topics Geometry
    Algebraic Geometry
  • Buy this book on publisher's site


“‘The goal of the book is to teach the reader new and classical methods for proving geometric inequalities.’ ... The book contains more than 1000 problems. ... intended for mathematics competitions and Olympiads. Every chapter contains problems for self-study and solutions.” (Sándor Nagydobai Kiss, zbMATH 1375.51001, 2018)