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.

### Table of Contents

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

### Sample Chapters

Preface

Sample Chapter 8

Chapter 8 Hints

Chapter 8 Solutions

Sample Chapter 12

Chapter 12 Hints

Chapter 12 Solutions

Chapter 14

Chapter 14 Maple Sheet

Errata

### 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.

### About the Authors

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...