Euclidean plane geometry is one of the oldest and most beautiful topics in mathematics. Instead of carefully building geometries from axiom sets, this book uses a wealth of methods to solve problems in Euclidean geometry. Many of these methods arose where existing techniques proved inadequate. In several cases, the new ideas used in solving specific problems later developed into independent areas of mathematics. This book is primarily a geometry textbook, but studying geometry in this way will also develop students' appreciation of the subject and of mathematics as a whole. For instance, despite the fact that the analytic method has been part of mathematics for four centuries, it is rarely a tool a student considers using when faced with a geometry problem. Methods for Euclidean Geometry explores the application of a broad range of mathematical topics to the solution of Euclidean problems.
• A unique and refreshing approach to teaching Euclidean geometry which will also serve to enhance a student's understanding of mathematics as a whole • Over a third of the book is given over to detailed problems of varying difficulty, and their solutions • Some of the same exercises are repeated in different chapters so that the student may see how the same problem may be tackled by a number of different methods
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. A+ne transformations; 13. Inversions; 14. Coordinate method with software.