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© 2016

The Universe of Conics

From the ancient Greeks to 21st century developments

Textbook

Table of contents

  1. Front Matter
    Pages i-viii
  2. Georg Glaeser, Hellmuth Stachel, Boris Odehnal
    Pages 1-10
  3. Georg Glaeser, Hellmuth Stachel, Boris Odehnal
    Pages 11-60
  4. Georg Glaeser, Hellmuth Stachel, Boris Odehnal
    Pages 61-126
  5. Georg Glaeser, Hellmuth Stachel, Boris Odehnal
    Pages 127-176
  6. Georg Glaeser, Hellmuth Stachel, Boris Odehnal
    Pages 177-216
  7. Georg Glaeser, Hellmuth Stachel, Boris Odehnal
    Pages 217-258
  8. Georg Glaeser, Hellmuth Stachel, Boris Odehnal
    Pages 259-350
  9. Georg Glaeser, Hellmuth Stachel, Boris Odehnal
    Pages 351-374
  10. Georg Glaeser, Hellmuth Stachel, Boris Odehnal
    Pages 375-434
  11. Georg Glaeser, Hellmuth Stachel, Boris Odehnal
    Pages 435-479
  12. Back Matter
    Pages 480-488

About this book

Introduction

This text presents the classical theory of conics in a modern form. It includes many novel results that are not easily accessible elsewhere. The approach combines synthetic and analytic methods to derive projective, affine and metrical properties, covering both Euclidean and non-Euclidean geometries.

With more than two thousand years of history, conic sections play a fundamental role in numerous fields of mathematics and physics, with applications to mechanical engineering, architecture, astronomy, design and computer graphics.

This text will be invaluable to undergraduate mathematics students, those in adjacent fields of study, and anyone with an interest in classical geometry.

Augmented with more than 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.


Authors

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.


Keywords

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

Authors and affiliations

  1. 1.Department of GeometryUniversity of Applied Arts ViennaViennaAustria
  2. 2.Inst. of Disc. Mathematics and GeometryVienna University of TechnologyViennaAustria
  3. 3.Department of GeometryUniversity of Applied Arts ViennaViennaAustria

About the authors

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.

Bibliographic information

  • Book Title The Universe of Conics
  • Book Subtitle From the ancient Greeks to 21st century developments
  • Authors Georg Glaeser
    Hellmuth Stachel
    Boris Odehnal
  • DOI https://doi.org/10.1007/978-3-662-45450-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 2016
  • Publisher Name Springer Spektrum, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-662-45449-7
  • Softcover ISBN 978-3-662-56881-1
  • eBook ISBN 978-3-662-45450-3
  • Edition Number 1
  • Number of Pages VIII, 488
  • Number of Illustrations 350 b/w illustrations, 0 illustrations in colour
  • Topics Geometry
    Applications of Mathematics
  • Buy this book on publisher's site

Reviews

“The hundreds of meticulously crafted and beautifully rendered figures … form the most attractive component of the book. … ‘The book has been written for people who love geometry and it is mainly based on figures and synthetic conclusions rather than on pure analytic calculations. In many proofs, illustrations help to explain ideas and to support the argumentation, and in a few cases, the picture can display a theorem at a glance together with its proof.’” (Tushar Das, MAA Reviews, maa.org, March, 2017)

“The main purpose of the book under review is to present definitions, main properties and applications of conics from different complementary viewpoints. … It is written primarily for a general–undergraduate–public … . the figures deserve a special mention: on one hand they help to explain the proofs and on the other they show the beauty of geometry and the elegance of mathematics.” (Roberto Muñoz, Mathematical Reviews, January, 2017)

“‘The universe of conics’ covers the most important properties of conics in an attempt to preserve at least parts of the knowledge that was accumulated over the last two millenia. … ‘The universe of conics’ is a must read for all who still speak geometry as well as for those who would like to learn this ancient language.” (Franz Lemmermeyer, zbMATH 1354.51001, 2017)

“This book is an innovative, masterful presentation of conic sections in both Euclidean and non-Euclidean geometries. It is beautifully illustrated with more than 360 full-color figures and photographs. … The text will interest both beginning students and readers with a strong mathematical background. The book concludes with a list of 70 references. Summing Up: Recommended. Upper-division undergraduates through researchers and faculty; professionals and practitioners.” (D. P. Turner, Choice, Vol. 54 (3), November, 2016)