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The Universe of Quadrics

This text presents the theory of quadrics in a modern form. It builds on the previously published book "The Universe of Conics", including many novel results that are not easily accessible elsewhere. As in the conics book, the approach combines synthetic and analytic methods to derive projective, affine, and metrical properties, covering both Euclidean and non-Euclidean geometries.

While the history of conics is more than two thousand years old, the theory of quadrics began to develop approximately three hundred years ago. Quadrics play a fundamental role in numerous fields of mathematics and physics, their applications ranging from mechanical engineering, architecture, astronomy, and design to computer graphics.

This text will be invaluable to undergraduate and graduate mathematics students, those in adjacent fields of study, and anyone with a deeper interest in geometry. Complemented with about 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.

The Universe of Quadrics

1 Introduction.- 2 Quadrics in Euclidean 3-space.- 3 Linear algebraic approach to quadrics.- 4 Projective and affine quadrics.- 5 Pencils of quadrics.- 6 Cubic and quartic space curves as intersections of quadrics.- 7 Confocal quadrics.- 8 Special problems.- 9 Quadrics and Differential Geometry.- 10 Line Geometry, Sphere Geometry, Kinematics.- 11 Some generalizations of quadrics.- References.- Index.