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BuchGebunden
606 Seiten
Englisch
Springererschienen am22.04.20201st ed. 2020
The Universe of QuadricsThis 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.mehr
Verfügbare Formate
BuchGebunden
EUR128,39
BuchKartoniert, Paperback
EUR90,94
E-BookPDF1 - PDF WatermarkE-Book
EUR90,94

Produkt

KlappentextThe Universe of QuadricsThis 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.
Zusammenfassung
Enriches understanding of a both classical and modern subject with a strong visual component

Shows recent results in an accesible way

Broadens your understanding of geometry as a whole
Details
ISBN/GTIN978-3-662-61052-7
ProduktartBuch
EinbandartGebunden
Verlag
Erscheinungsjahr2020
Erscheinungsdatum22.04.2020
Auflage1st ed. 2020
Seiten606 Seiten
SpracheEnglisch
Gewicht1240 g
IllustrationenVIII, 606 p. 300 illus. in color.
Artikel-Nr.47831753

Inhalt/Kritik

Inhaltsverzeichnis
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.mehr
Kritik
"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)mehr

Autor

The Authors

Boris Odehnal, born in 1973, got his PhD and habilitation in geometry at the Vienna University of Technology. 2011-2012 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 1980-2011, 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.