College Geometry: A Unified Development (Textbooks in Mathematics)

About this book

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 Einsteins relativity and theories of cosmology.