**Mathematical World**

Volume: 26;
2007;
134 pp;
Softcover

MSC: Primary 51;

Print ISBN: 978-0-8218-4323-9

Product Code: MAWRLD/26

List Price: $29.00

Individual Member Price: $23.20

**Electronic ISBN: 978-1-4704-2481-7
Product Code: MAWRLD/26.E**

List Price: $29.00

Individual Member Price: $23.20

# Geometry of Conics

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*A. V. Akopyan; A. A. Zaslavsky*

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.

#### Readership

Undergraduate and graduate students interested in geometry.

#### Reviews & Endorsements

The book is well written and contains a lot of figures illustrating the theorems and their proofs.

-- MAA Reviews

#### Table of Contents

# Table of Contents

## Geometry of Conics

- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Contents v6 free
- Preface vii8 free
- Chapter 1. Elementary Properties of Curves of Second Degree 110 free
- 1.1. Definitions 110
- 1.2. Analytic definition and classification of curves of second degree 514
- 1.3. The optical property 615
- 1.4. The isogonal property of conics 1019
- 1.5. Curves of second degree as projections of the circle 1524
- 1.6. The eccentricity and yet another definition of conies 1726
- 1.7. Some remarkable properties of the parabola 1928

- Chapter 2. Some Results from Classical Geometry 2736
- Chapter 3. Projective Properties of Conics 6574
- Chapter 4. Euclidean Properties of Curves of Second Degree 99108
- Chapter 5. Solutions to the Problems 119128
- Bibliography 131140
- Index 133142
- Back Cover Back Cover1145