By David C. Kay
Designed for arithmetic majors and different scholars who intend to coach arithmetic on the secondary college point, College Geometry: A Unified Development unifies the 3 classical geometries inside of an axiomatic framework. the writer develops the axioms to incorporate Euclidean, elliptic, and hyperbolic geometry, exhibiting how geometry has genuine and far-reaching implications. He techniques each subject as a clean, new thought and thoroughly defines and explains geometric principles.
The ebook starts with straightforward principles approximately issues, traces, and distance, steadily introducing extra complex thoughts reminiscent of congruent triangles and geometric inequalities. on the center of the textual content, the writer at the same time develops the classical formulation for round and hyperbolic geometry in the axiomatic framework. He explains how the trigonometry of the perfect triangle, together with the Pythagorean theorem, is constructed for classical non-Euclidean geometries. formerly available simply to complicated or graduate scholars, this fabric is gifted at an user-friendly point. The publication additionally explores different vital strategies of contemporary geometry, together with affine differences and round inversion.
Through transparent factors and various examples and difficulties, this article exhibits step by step how basic geometric rules are hooked up to complicated geometry. It represents step one towards destiny examine of Riemannian geometry, Einstein’s relativity, and theories of cosmology.
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Extra resources for College Geometry: A Unified Development (Textbooks in Mathematics)
College Geometry: A Unified Development (Textbooks in Mathematics) by David C. Kay
Categories: Number Theory