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, Einsteinas relativity, and theories of cosmology.The famous book by Nathan A. Court, College Geometry (1952), used for many years for courses by that same title for teachers and ... The authora#39;s original book by that title (published in 1969 by Holt, Rinehart, and Winston, out of print for many years) attempted to embrace much of ... common axiomatic basis in just 11 axioms in the authora#39;s 1969 book. ... The aplota becomes more involved in Chapter 3 where much of the basic geometry normally encountered in a high school course isanbsp;...
|Author||:||David C. Kay|
|Publisher||:||CRC Press - 2011-06-24|