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Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | 30000010283092 | QA474 B94 2010 f | Open Access Book | Folio Book | Searching... |
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Summary
Summary
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.
Reviews 1
Choice Review
Experienced mathematics teachers Byer and Smeltzer (both, Eastern Mennonite Univ.) and Lazebnik (Univ. of Delaware) have written an undergraduate mathematics course resource suitable for upper-division students and future teachers. The focus is on solving problems in Euclidean geometry rather than on the formal axiomatic approach to geometry or on different types of geometry. The book includes standard topics in Euclidean geometry (axioms, lines and polygons, circles, measurement, conic sections, and loci). The additional subjects covered (trigonometry, coordinate geometry, complex numbers, vectors, affine transformations, and inversions) are for solving problems in Euclidean geometry, rather than for their own intrinsic merit. The authors thoroughly cover all of these topics. Although the historical and motivational material is weak, disorganized, uninspired, and sometimes confusing, the book is an excellent source of problems for teachers and students. A third of the volume consists of solutions to all of the chapter problems; a nice feature is a section of hints that is separate from the complete solutions. Summing Up: Recommended. Upper-division undergraduates and faculty. C. A. Gorini Maharishi University of Management
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 A+ne transformations |
| 13 Inversions |
| 14 Coordinate method with software |
