THE FOUNDATIONS OF GEOMETRY is a textbook for an undergraduate course in axiomatic geometry. The course is suitable for all mathematics majors, including those who plan to become high school mathematics teachers. The textbook implements the recent recommendations regarding "The Mathematical Education of Teachers" within the context of a traditional axiomatic treatment of geometry. In addition to all the standard topics (Euclid's Elements, axiomatic systems, the parallel postulates, neutral geometry, Euclidean geometry, hyperbolic geometry, constructions, transformations, and the classical models for non-Euclidean geometry), the book also includes a chapter on polygonal models for the hyperbolic plane and the geometry of space.
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Title: THE FOUNDATIONS OF GEOMETRY Author: Gerard A. Venema ISBN: 0-13-143700-3 Publisher: Prentice Hall (now Pearson) Publication date: January, 2005 Copyright: 2006 Format: Paper; 448 pp List price: $84.00 More information about the book is available in the Prentice Hall catalog. If you wish to obtain a copy, you can either order one directly from the publisher or from a bookseller such as Amazon.com. The cover art is by Victor Vasarely, Hungarian-born French abstract painter, 1908-1997. |
A supplement entitled Exploring Advanced Euclidean Geometry with GeoGebra was published by the Mathematical Association of America (MAA) in 2013. This book can be used either as a lab manual to supplement a course taught from The Foundations of Geometry, Second Edition or as a stand-alone introduction to advanced topics in Euclidean geometry. The book utilizes dynamic geometry software, specifically GeoGebra, to explore the statements and proofs of many of the most interesting theorems in advanced Euclidean geometry. The text begins with a short but complete introduction to GeoGebra; the remainder of the text consists almost entirely of exercises that guide students as they discover the mathematics and then come to understand it for themselves. It covers such topics as triangle centers, circumscribed and inscribed circles, medial and orthic triangles, the nine-point circle, the theorems of Ceva and Menelaus, and many applications of the theorems of Menelaus and Ceva. It also includes chapters on Euclidean inversions and the Poincaré disk.
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