The Universe of Conics: From the ancient Greeks to 21st century developments

Description

This text presents the classical theory of conics in a modern form. It includes many novel results that are not easily accessible elsewhere. The approach combines synthetic and analytic methods to derive projective, affine and metrical properties, covering both Euclidean and non-Euclidean geometries. With more than two thousand years of history, conic sections play a fundamental role in numerous fields of mathematics and physics, with applications to mechanical engineering, architecture, astronomy, design and computer graphics. This text will be invaluable to undergraduate mathematics students, those in adjacent fields of study, and anyone with an interest in classical geometry. Augmented with more than three hundred fifty figures and photographs, this innovative text will enhance your understanding of projective geometry, linear algebra, mechanics, and differential geometry, with careful exposition and many illustrative exercises. Front Matter....Pages i-viii Introduction....Pages 1-10 Euclidean plane....Pages 11-60 Differential Geometry....Pages 61-126 Euclidean 3-space....Pages 127-176 Projective Geometry....Pages 177-216 Projective conics....Pages 217-258 Polarities and pencils....Pages 259-350 Affine Geometry....Pages 351-374 Special problems....Pages 375-434 Other geometries....Pages 435-479 Back Matter....Pages 480-488