El. knyga: College Geometry: A Unified Development

As intimated by its title, this undergraduate textbook in geometry seeks to provide a unified framework for understanding the three classical geometries within a wider mathematics cannon that connects students to core historical studies while still allowing for the exploration of new and cutting edge research. The work examines Euclidean, elliptic and hyperbolic geometries, beginning with basic concepts and provides students with example problems that build in complexity. Appendices providing advanced examples and sample equations are included. Kay is a retired professor of mathematics. Annotation ©2011 Book News, Inc., Portland, OR (booknews.com)

Connecting fundamental geometric ideas to advanced geometry, this text unifies Euclidean, elliptic, and hyperbolic geometry within an axiomatic framework. It covers topological shapes of geometric objects and includes more than 700 carefully crafted problems. Numerous examples show how geometry has real and far-reaching implications. The author approaches every topic as a fresh, new concept and carefully defines and explains geometric principles. He also offers instructions on specific experiments using the Geometer’s Sketchpad software. A solutions manual is available upon qualified course adoption.

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.