Boris Odehnal, Hellmuth Stachel, Georg Glaeser

The Universe of Quadrics

• Gebundenes Buch

Produktbeschreibung

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.

Produktdetails

• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 978-3-662-61052-7
• 1st ed. 2020
• Seitenzahl: 616
• Erscheinungstermin: 22. April 2020
• Englisch
• Abmessung: 246mm x 173mm x 37mm
• Gewicht: 1240g
• ISBN-13: 9783662610527
• ISBN-10: 3662610523
• Artikelnr.: 58444611

Autorenporträt

Hellmuth Stachel, born 1942, got his PhD and habilitation in geometry in Graz. 1978 full professor at the Mining University Leoben, 1980-2011 full professor of geometry at the Vienna University of Technology. Coauthor of several books on mathematics and computational geometry and of more than 120 articles on geometry. Georg Glaeser, born 1955, got his PhD and habilitation in geometry at the Vienna University of Technology. Since 1998 full professor of geometry at the University of Applied Arts Vienna. Author and coauthor of more than a dozen books on geometry, mathematics, computational geometry, computer graphics, and photography. Boris Odehnal, born 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 lecturer of geometry at the University of Applied Arts Vienna. Author of several dozens of publications on geometry.

Inhaltsangabe

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.

Rezensionen

"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)