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.
Translated into many languages, this book was in continuous use as the standard university-level text for a quarter-century, until it was revised and enlarged by the author in 1952.
An important difference of this book from the majority of modern college geometry texts is that it avoids axiomatics. The students using this book have had very little experience with formal mathematics.
Elementary College Geometry
College Geometry is divided into two parts.
This is the eBook of the printed book and may not include any media, website access codes, or print supplements that may come packaged with the bound book.
To make learning interactive and enjoyable, this new edition includes exciting new features such as Technology Connections and Hands-on Activities. Knowledge of beginning algebra and a scientific calculator are required for this text.
Introduction to vector algebra in the plane; circles and coaxial systems; mappings of the Euclidean plane; similitudes, isometries, Moebius transformations, much more. Includes over 500 exercises.
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The book's discovery-based approach guides students to explore geometric worlds through computer-based activities, enabling students to make observations, develop conjectures, and write mathematical proofs.
The book's truly discovery-based approach guides readers to learn geometry through explorations of topics ranging from triangles and circles to transformational, taxicab, and hyperbolic geometries.