An Excursion through Elementary Mathematics, Volume II

1. Front Matter

   Pages i-xi

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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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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.

• Euclidean geometry
• Geometry
• Solids
• Trigonometry
• Problem solving
• Mathematics Olympiad
• IMO

“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)

• Universidade Federal do Ceará, Fortaleza, Brazil

  Antonio Caminha Muniz Neto

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.

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