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Universe of Quadrics 1st ed. 2020 [Kietas viršelis]

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  • Formatas: Hardback, 606 pages, aukštis x plotis: 240x168 mm, weight: 1392 g, 300 Illustrations, color; VIII, 606 p. 300 illus. in color., 1 Hardback
  • Išleidimo metai: 22-Apr-2020
  • Leidėjas: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3662610523
  • ISBN-13: 9783662610527
Kitos knygos pagal šią temą:
Universe of Quadrics 1st ed. 2020Didesnis paveikslėlis
  • Formatas: Hardback, 606 pages, aukštis x plotis: 240x168 mm, weight: 1392 g, 300 Illustrations, color; VIII, 606 p. 300 illus. in color., 1 Hardback
  • Išleidimo metai: 22-Apr-2020
  • Leidėjas: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3662610523
  • ISBN-13: 9783662610527
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9783662610527.html
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.

Recenzijos

The Universe of Quadrics (UQ) is the beautifully written sequel to the authors 2016 The Universe of Conics (UC), which was also a pleasure to review. Throughout UQ there is constant reference to UC and I would recommend readers interested in diving in these waters to have both texts close. (Tushar Das, MAA Reviews, April 16, 2023)

The authors of this marvelous book . Given the enormous wealth of results it contains . It is clearly a labor of love, and if the subject has any chance of gaining readers, then this book is its best chance, given not only the care with which everything is presented, in a self-contained manner, but also the wealth of stunning multi-colored figures of the highest quality. (Victor V. Pambuccian, Mathematical Reviews, March, 2022)

1 Introduction
1(6)
2 Quadrics in Euclidean 3-space
7(84)
2.1 Ellipsoids
11(15)
2.2 Hyperboloids
26(26)
2.3 Paraboloids
52(18)
2.4 Shared metric properties
70(10)
2.5 Flexible models of quadrics
80(11)
3 Linear algebraic approach to quadrics
91(28)
3.1 Principal-axes transformation in En
92(20)
3.2 Quadrics in the Euclidean plane and 3-space
112(7)
4 Projective and affine quadrics
119(58)
4.1 Three-dimensional Projective Geometry
120(17)
4.2 Polarities
137(20)
4.3 The projective n-space
157(8)
4.4 Projective models of non-Euclidean geometries
165(12)
5 Pencils of quadrics
177(28)
5.1 Definition of pencils, basics, invariants
179(12)
5.2 Principal points and common polar tetrahedron
191(1)
5.3 Desargues's involution theorem
191(2)
5.4 Dual pencils
193(2)
5.5 Special pencils
195(10)
6 Cubic and quartic space curves as intersections of quadrics
205(74)
6.1 Standard cubic
207(5)
6.2 Quadrics containing a cubic
212(14)
6.3 Osculating planes of a cubic
226(8)
6.4 An analogue to Steiner's generation
234(2)
6.5 Chords of a cubic
236(2)
6.6 The cubic of coincidence - points with coinciding images
238(3)
6.7 Projection with the chords of a cubic
241(4)
6.8 Cross ratios and projective automorphisms
245(2)
6.9 Quartic space curves
247(32)
7 Confocal quadrics
279(48)
7.1 The families of confocal quadrics
280(14)
7.2 Ivory's Theorem and bipartite frameworks
294(25)
7.3 String constructions of quadrics
319(8)
8 Special problems
327(56)
8.1 Reflection in quadratic surfaces
328(12)
8.2 Moving conies on quadrics
340(20)
8.3 Quadrics on skew quadrilaterals
360(8)
8.4 Rational parametrizations, quadrics as Bezier surfaces
368(15)
9 Quadrics and Differential Geometry
383(92)
9.1 Curvature functions on quadrics
385(13)
9.2 Quadrics as ruled surfaces
398(15)
9.3 Lie's osculating quadric
413(4)
9.4 Normals to a quadric
417(40)
9.5 Curves of constant slope on quadrics
457(10)
9.6 Geodesies on quadrics
467(8)
10 Line Geometry, Sphere Geometry, Kinematics
475(86)
10.1 Line Geometry
477(42)
10.2 Sphere Geometry
519(14)
10.3 Kinematics
533(28)
11 Some generalizations of quadrics
561(26)
11.1 Miiller's cubic surface
563(4)
11.2 Superquadrics
567(7)
11.3 Surfaces of osculating circles
574(3)
11.4 Plikker's conoid
577(2)
11.5 Sum and product of distances to fixed points
579(8)
References 587(8)
Index 595
The Authors

Boris Odehnal, born in 1973, got his PhD and habilitation in geometry at the Vienna University of Technology. 20112012 professor at the Dresden University of Technology. Since 2012, he has held the position of senior lecturer in geometry at the University of Applied Arts Vienna. He is the author of several dozens of publications on geometry.

Hellmuth Stachel, born in 1942, got his PhD and habilitation in geometry in Graz. In 1978, he became full professor at the Mining University Leoben, and from 19802011, he was full professor of geometry at the Vienna University of Technology. He has coauthored several books on mathematics and computational geometry and more than 160 articles on geometry.

Georg Glaeser, born in 1955, got his PhD and habilitation in geometry at the Vienna University of Technology. Since 1998, he is full professor of geometry at the University of Applied Arts Vienna. He is the author and coauthor of more than twenty books on geometry,mathematics, computational geometry, computer graphics, and photography.