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The Universe of Quadrics

Benefits

  • 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

Textbook

Table of contents

  1. Front Matter
    Pages i-viii
  2. Boris Odehnal, Hellmuth Stachel, Georg Glaeser
    Pages 1-6
  3. Boris Odehnal, Hellmuth Stachel, Georg Glaeser
    Pages 7-90
  4. Boris Odehnal, Hellmuth Stachel, Georg Glaeser
    Pages 91-118
  5. Boris Odehnal, Hellmuth Stachel, Georg Glaeser
    Pages 119-175
  6. Boris Odehnal, Hellmuth Stachel, Georg Glaeser
    Pages 177-204
  7. Boris Odehnal, Hellmuth Stachel, Georg Glaeser
    Pages 205-277
  8. Boris Odehnal, Hellmuth Stachel, Georg Glaeser
    Pages 279-325
  9. Boris Odehnal, Hellmuth Stachel, Georg Glaeser
    Pages 327-381
  10. Boris Odehnal, Hellmuth Stachel, Georg Glaeser
    Pages 383-474
  11. Boris Odehnal, Hellmuth Stachel, Georg Glaeser
    Pages 475-559
  12. Boris Odehnal, Hellmuth Stachel, Georg Glaeser
    Pages 561-586
  13. Back Matter
    Pages 587-606

About this book

Introduction

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 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.


Keywords

Applications Classical Geometry Conics Differential Geometry Geometry History of Mathematics Projective Geometry

Authors and affiliations

  1. 1.Department of GeometryUniversity of Applied Arts Vienna Department of GeometryViennaAustria
  2. 2.Institute of Discrete Mathematics and GeometryVienna University of Technology Institute of Discrete Mathematics and GeometryViennaAustria
  3. 3.Department of GeometryUniversity of Applied Arts Vienna Department of GeometryViennaAustria

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