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An Excursion through Elementary Mathematics, Volume II

Euclidean Geometry

  • Textbook
  • © 2018

Overview

Authors:
  1. Antonio Caminha Muniz Neto

    1. Universidade Federal do Ceará, Fortaleza, Brazil

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  • Combines an in-depth overview of the theory with problems presented at several Mathematical Olympiads around the world
  • Offers a comprehensive course on problem-solving techniques
  • Presents a coherent development of mathematical ideas and methods behind problem solving
  • Brings several classical, relevant results of various fields in mathematics

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

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Basic Geometric Concepts

    • Antonio Caminha Muniz Neto
    Pages 1-17

  3. Congruence of Triangles

    • Antonio Caminha Muniz Neto
    Pages 19-59

  4. Loci in the Plane

    • Antonio Caminha Muniz Neto
    Pages 61-99

  5. Proportionality and Similarity

    • Antonio Caminha Muniz Neto
    Pages 101-150

  6. Area of Plane Figures

    • Antonio Caminha Muniz Neto
    Pages 151-180

  7. The Cartesian Method

    • Antonio Caminha Muniz Neto
    Pages 181-225

  8. Trigonometry and Geometry

    • Antonio Caminha Muniz Neto
    Pages 227-268

  9. Vectors in the Plane

    • Antonio Caminha Muniz Neto
    Pages 269-287

  10. A First Glimpse on Projective Techniques

    • Antonio Caminha Muniz Neto
    Pages 289-329

  11. Basic Concepts in Solid Geometry

    • Antonio Caminha Muniz Neto
    Pages 331-375

  12. Some Simple Solids

    • Antonio Caminha Muniz Neto
    Pages 377-402

  13. Convex Polyhedra

    • Antonio Caminha Muniz Neto
    Pages 403-426

  14. Volume of Solids

    • Antonio Caminha Muniz Neto
    Pages 427-447

  15. Hints and Solutions

    • Antonio Caminha Muniz Neto
    Pages 449-534

  16. Back Matter

    Pages 535-550
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Keywords

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 problemspresented 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.

Reviews

“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)

Authors and Affiliations

  • Universidade Federal do Ceará, Fortaleza, Brazil

    Antonio Caminha Muniz Neto

About the author

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

  • DOI: https://doi.org/10.1007/978-3-319-77974-4

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing AG, part of Springer Nature 2018

  • Hardcover ISBN: 978-3-319-77973-7Published: 26 April 2018

  • Softcover ISBN: 978-3-030-08589-6Published: 14 December 2018

  • eBook ISBN: 978-3-319-77974-4Published: 16 April 2018

  • Series ISSN: 0941-3502

  • Series E-ISSN: 2197-8506

  • Edition Number: 1

  • Number of Pages: XI, 550

  • Number of Illustrations: 411 b/w illustrations

  • Topics: Convex and Discrete Geometry, Polytopes, Projective Geometry

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