An Excursion through Elementary Mathematics, Volume II: Euclidean Geometry

by Antonio Caminha Muniz Neto

Overview

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.

Product Details

ISBN-13:	9783319779737
Publisher:	Springer International Publishing
Publication date:	04/17/2018
Series:	Problem Books in Mathematics
Edition description:	1st ed. 2018
Pages:	550
Product dimensions:	6.10(w) x 9.25(h) x (d)

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.

Table of Contents

Chapter 01- Basic Geometric Concepts.- Chapter 02- Congruence of Triangles.- Chapter 03- Loci in the Plane.- Chapter 04- Proportionality and Similarity.- Chapter 05- Area of Plane Figures.- Chapter 06- The Cartesian Method.- Chapter 07- Trigonometry and Geometry.- Chapter 08- Vectors in the Plane.- Chapter 09- A First Glimpse on Projective Techniques.- Chapter 10- Basic Concepts in Solid Geometry.- Chapter 11- Some Simple Solids.- Chapter 12- Convex Polyhedra.- Chapter 13- Volume of Solids.- Chapter 14- Hints and Solutions.

Editorial 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)

From the Publisher