College Geometry: A Unified Development

David C. Kay

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June 24, 2011 by CRC Press
Textbook - 652 Pages - 657 B/W Illustrations
ISBN 9781439819111 - CAT# K11008
Series: Textbooks in Mathematics

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Features

  • Covers topological shapes of geometric objects
  • Includes "Moments for Reflection" sections that challenge students to think for themselves and encourage self-discovery
  • Offers instructions on specific experiments using the Geometer’s Sketchpad software
  • Contains more than 500 drawings and 80 examples to illustrate concepts and problem solving
  • Presents historical notes that point out the human aspects of geometric discovery
  • Incorporates research projects for undergraduate students
  • Provides more than 700 carefully crafted problems, with selected solutions at the back of the book

Solutions manual available for qualifying instructors

Summary

Designed for mathematics majors and other students who intend to teach mathematics at the secondary school level, College Geometry: A Unified Development unifies the three classical geometries within an axiomatic framework. The author develops the axioms to include Euclidean, elliptic, and hyperbolic geometry, showing how geometry has real and far-reaching implications. He approaches every topic as a fresh, new concept and carefully defines and explains geometric principles.

The book begins with elementary ideas about points, lines, and distance, gradually introducing more advanced concepts such as congruent triangles and geometric inequalities. At the core of the text, the author simultaneously develops the classical formulas for spherical and hyperbolic geometry within the axiomatic framework. He explains how the trigonometry of the right triangle, including the Pythagorean theorem, is developed for classical non-Euclidean geometries. Previously accessible only to advanced or graduate students, this material is presented at an elementary level. The book also explores other important concepts of modern geometry, including affine transformations and circular inversion.

Through clear explanations and numerous examples and problems, this text shows step-by-step how fundamental geometric ideas are connected to advanced geometry. It represents the first step toward future study of Riemannian geometry, Einstein’s relativity, and theories of cosmology.