Geometry of Conics
About this Title
A. V. Akopyan and A. A. Zaslavsky, CEMI RAN, Moscow, Russia. Translated by Alex Martsinkovsky
Publication: Mathematical World
Publication Year 2007: Volume 26
ISBNs: 978-0-8218-4323-9 (print); 978-1-4704-2481-7 (online)
MathSciNet review: MR2359987
MSC: Primary 51-02; Secondary 51M04
The book is devoted to the properties of conics (plane curves of second degree) that can be formulated and proved using only elementary geometry. Starting with the well-known optical properties of conics, the authors move to less trivial results, both classical and contemporary. In particular, the chapter on projective properties of conics contains a detailed analysis of the polar correspondence, pencils of conics, and the Poncelet theorem. In the chapter on metric properties of conics the authors discuss, in particular, inscribed conics, normals to conics, and the Poncelet theorem for confocal ellipses.
The book demonstrates the advantage of purely geometric methods of studying conics. It contains over 50 exercises and problems aimed at advancing geometric intuition of the reader. The book also contains more than 100 carefully prepared figures, which will help the reader to better understand the material presented.
Undergraduate and graduate students interested in geometry.
Table of Contents
- Chapter 1. Elementary properties of curves of second degree
- Chapter 2. Some results from classical geometry
- Chapter 3. Projective properties of conics
- Chapter 4. Euclidean properties of curves of second degree
- Chapter 5. Solutions to the problems