Overview
- 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
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About this book
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.
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Keywords
Table of contents (11 chapters)
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Front Matter
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Back Matter
Reviews
“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)
Authors and Affiliations
About the authors
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.
Bibliographic Information
Book Title: The Universe of Quadrics
Authors: Boris Odehnal, Hellmuth Stachel, Georg Glaeser
DOI: https://doi.org/10.1007/978-3-662-61053-4
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag GmbH Germany, part of Springer Nature 2020
Hardcover ISBN: 978-3-662-61052-7Published: 22 April 2020
Softcover ISBN: 978-3-662-61055-8Published: 23 April 2021
eBook ISBN: 978-3-662-61053-4Published: 21 April 2020
Edition Number: 1
Number of Pages: VIII, 606
Number of Illustrations: 300 illustrations in colour
Topics: Geometry, Applications of Mathematics