© 2018

An Excursion through Elementary Mathematics, Volume II

Euclidean Geometry


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

Table of contents

  1. Front Matter
    Pages i-xi
  2. Antonio Caminha Muniz Neto
    Pages 1-17
  3. Antonio Caminha Muniz Neto
    Pages 19-59
  4. Antonio Caminha Muniz Neto
    Pages 61-99
  5. Antonio Caminha Muniz Neto
    Pages 101-150
  6. Antonio Caminha Muniz Neto
    Pages 151-180
  7. Antonio Caminha Muniz Neto
    Pages 181-225
  8. Antonio Caminha Muniz Neto
    Pages 227-268
  9. Antonio Caminha Muniz Neto
    Pages 269-287
  10. Antonio Caminha Muniz Neto
    Pages 289-329
  11. Antonio Caminha Muniz Neto
    Pages 331-375
  12. Antonio Caminha Muniz Neto
    Pages 377-402
  13. Antonio Caminha Muniz Neto
    Pages 403-426
  14. Antonio Caminha Muniz Neto
    Pages 427-447
  15. Antonio Caminha Muniz Neto
    Pages 449-534
  16. Back Matter
    Pages 535-550

About this book


This book provides a comprehensive, in-depth overview of elementary mathematics as explored in Mathematical Olympiads around the world. It expands on topics usually encountered in high school and could even be used as preparation for a first-semester undergraduate course. This second volume covers Plane Geometry, Trigonometry, Space Geometry, Vectors in the Plane, Solids and much more.

As part of a collection, the book differs from other publications in this field by not being a mere selection of questions or a set of tips and tricks that applies to specific problems. It starts from the most basic theoretical principles, without being either too general or too axiomatic. Examples and problems are discussed only if they are helpful as applications of the theory. Propositions are proved in detail and subsequently applied to Olympic problems or to other problems at the Olympic level.

The book also explores some of the hardest problems presented at National and International Mathematics Olympiads, as well as many essential theorems related to the content. An extensive Appendix offering hints on or full solutions for all difficult problems rounds out the book.


Euclidean geometry Geometry Solids Trigonometry Problem solving Mathematics Olympiad IMO

Authors and affiliations

  1. 1.Universidade Federal do CearáFortalezaBrazil

About the authors

Antonio Caminha M. Neto received his PhD from the Federal University of Ceará, Brazil in 2004. In the same year he joined the University as a Professor of Mathematics, where he is now a member of the Differential Geometry Research Group. The author of several research papers, Caminha was distinguished by a CNPq Research Grant on Differential Geometry. He is also an Affiliate Member of the Brazilian Academy of Sciences. Prior to his academic career, Caminha was himself an Olympic competitor, who has placed 4th in the 1990 Brazilian Mathematical Olympiad. Subsequently, as a high school teacher in the 1990s, he coached Brazilian students in preparation for various mathematical competitions, from regional meets to the Iberoamerican Mathematical Olympiad and the International Mathematical Olympiad, where several of them were medalists. He was also a Leader of the Brazilian Team at the 1996 and 1999 South Cone Mathematical Olympiad, and Deputy Leader of the Brazilian Team at the 1995 and 2001 International Mathematical Olympiads. In 2012, Caminha published a six-volume book collection entitled Topics in Elementary Mathematics with the Brazilian Mathematical Society, which gave rise to this book. He also published a book on selected topics on Differential Geometry, especially the Bochner method and harmonic maps.

Bibliographic information

  • Book Title An Excursion through Elementary Mathematics, Volume II
  • Book Subtitle Euclidean Geometry
  • Authors Antonio Caminha Muniz Neto
  • Series Title Problem Books in Mathematics
  • Series Abbreviated Title Problem Books Mathematics
  • DOI
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-319-77973-7
  • Softcover ISBN 978-3-030-08589-6
  • eBook ISBN 978-3-319-77974-4
  • Series ISSN 0941-3502
  • Series E-ISSN 2197-8506
  • Edition Number 1
  • Number of Pages XI, 550
  • Number of Illustrations 411 b/w illustrations, 0 illustrations in colour
  • Topics Convex and Discrete Geometry
    Projective Geometry
  • Buy this book on publisher's site


“The authors provides an overview of elementary geometry in relationship with questions from mathematical Olympiads around the world. … The book also explores some problems proposed at various national and international mathematics Olympiads. This book is useful for high-school students interested in preparing for mathematical Olympiads.” (Teodora-Liliana Rǎdulescu, zbMATH 1395.51001, 2018)