Methods for Euclidean Geometry

By Owen Byer, Felix Lazebnik, and Deirdre L. Smeltzer

Catalog Code: MEG
ISBN: 978-0-88385-763-2
480 pp., Hardbound, 2010
List Price: $69.95 Member Price:$55.95
Series: Classroom Resource Materials

Euclidean plane geometry is one of the oldest and most beautiful of subjects in mathematics, and Methods for Euclidean Geometry explores the application of a broad range of mathematical techniques to the solution of Euclidean problems.

The book presents numerous problems of varying difficulty and diverse methods for solving them. More than a third of the book is devoted to problem statements, hints, and complete solutions. Some exercises are repeated in several chapters so that students can understand that there are various ways to solve them.

The book offers a unique and refreshing approach to teaching Euclidean geometry, which can serve to enhance students' understanding of mathematics as a whole.

1. Early History
2. Axioms: from Euclid to Today
3. Lines and Polygons
4. Circles
5. Length and Area
6. Loci
7. Trigonometry
8. Coordinatization
9. Conics
10. Complex numbers
11. Vectors
12. Affine Transformations
13. Inversions
14. Coordinate Method with Software
Epilogue
Hints to Chapter Problems
Solutions to Chapter Problems
Bibliography
Index

Excerpt: Loci (p. 107)

Having completed a survey of lines, polygons, circles, and angles, we come to another collection of well-known figures in the plane: ellipses, parabolas, and hyperbolas. In what situations do these figures appear? What is our motivation for studying them?

One way in which these figures arise quite naturally is when we try to find answers to questions of the type, "What is the set of all points (loci) of a plane that satisfy a given property?" Another is when we wish to understand the trajectory of a moving point. Yet a third situation occurs when we seek to describe the intersection of two surfaces in space.

Owen Byer (Eastern Mennonite University, Virginia), Felix Lazebnik (University of Delaware), and Deirdre L. Smeltzer (Eastern Mennonite University, Virginia) are members of the MAA.

MAA Review

Methods for Euclidean Geometry is a college geometry textbook with a unique mission. Instead of treating the subject as a distinct unit in the math curriculum, the authors integrate a variety of mathematical disciplines to engage and enlighten the reader. The text begins with an early history of geometry and then introduces and explains the basics of an axiomatic system. After this fairly extensive introduction, there are eleven chapters of content, ranging from lines and polygons to conics and inversions. The content is accompanied by numerous practice and supplemental exercises; solutions are included. Continued...