Inversions

I. Ya. Bakel’man, Joan W. Teller, Susan Williams9780226034997, 0226034992

In this book, I. Ya Bakel’man introduces inversion transformations in the Euclidean plane and discusses the interrelationships among more general mathematical concepts.

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Table of contents :
Front cover……Page 1
Back cover……Page 2
Table of Contents……Page 6
Preface……Page 7
1.1. Elementary Transformations of the Plane……Page 9
1.2. Stereographic Projection: The Point at Infinity of a Plane……Page 14
1.3. Inversions……Page 16
1.4. Properties of Inversions……Page 19
1.5. The Power of a Point with Respect to a Circle: The Radical Axis of Two Circles……Page 27
1.6. Application of Inversions to the Solution of Construction Problems……Page 32
1.7. Pencils of Circles……Page 40
1.8. Structure of an Elliptical Pencil……Page 48
1.9. Structure of a Parabolic Pencil……Page 49
1.10. Structure of a Hyperbolic Pencil……Page 50
1.11. Ptolemy’s Theorem……Page 53
2.1. Geometric Representation of Complex Numbers & Operations on Them……Page 56
2.2. Linear Functions of a Complex Variable & Elementary Transformations of the Plane……Page 60
2.3. Linear Fractional Functions of a Complex Variable & Related Pointwise Transformations of the Plane……Page 62
3.1. The Geometry of a Group of Transformations……Page 66
3.2. Euclidean Geometry……Page 72
3.3. Lobachevskian Geometry……Page 76