College Geometry - A Unified Development

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.Table of ContentLines, Distance, Segments, and Rays. Angles, Angle Measure, and Plane Separation. Unified Geometry: Triangles and Congruence. Quadrilaterals, Polygons, and Circles. Three Geometries. Inequalities for Quadrilaterals: Unified Trigonometry. Beyond Euclid: Modern Geometry. Transformations in Modern Geometry. Non-Euclidean Geometry: Analytical Approach. Appendices. Solutions to Selected Problems. Bibliography. Index.Review Quote"The book is a comprehensive textbook on basic geometry. … Key features of the book include numerous figures and many problems, more than half of which come with hints or even complete solutions. Frequent historical comments add to making the reading a pleasant one."—Michael Joswig, Zentralblatt MATH 1273Biographical NoteNow retired, David C. Kay was a professor and chairman of the Department of Mathematics at the University of North Carolina–Asheville for 14 years. He previously taught at the University of Oklahoma for 17 years. His research interests include distance geometry, convexity theory, and related functional analysis.