Geometric Transformations
Volume 4. Circular Transformations
£34.99
Part of Anneli Lax New Mathematical Library
- Author: I. M. Yaglom
- Translator: Abe Shenitzer
- Date Published: October 2009
- availability: This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.
- format: Paperback
- isbn: 9780883856482
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The familiar plane geometry of secondary school - figures composed of lines and circles - takes on a new life when viewed as the study of properties that are preserved by special groups of transformations. No longer is there a single, universal geometry: different sets of transformations of the plane correspond to intriguing, disparate geometries. This book is the concluding Part IV of Geometric Transformations, but it can be studied independently of Parts I, II, and III. The present Part IV develops the geometry of transformations of the plane that map circles to circles (conformal or anallagmatic geometry). The notion of inversion, or reflection in a circle, is the key tool employed. Applications include ruler-and-compass constructions and the Poincaré model of hyperbolic geometry. The straightforward, direct presentation assumes only some background in elementary geometry and trigonometry.
Read more- Numerous exercises lead the reader to a mastery of the methods and concepts
- The second half of the book contains detailed solutions of all the problems
- Accessible to undergraduates - assumes only familiarity with elementary geometry and trigonometry
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×Product details
- Date Published: October 2009
- format: Paperback
- isbn: 9780883856482
- length: 293 pages
- dimensions: 229 x 153 x 15 mm
- weight: 0.4kg
- availability: This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.
Table of Contents
1. Reflection in a circle (inversion)
Notes to Section 1
2. Application of inversions to the solution of construction
Problems: constructions with compass alone
Problems involving the construction of circles
Notes to Section 2
3. Pencils of circles. The radical axis of two circles
Notes to Section 3
4. Inversion (concluding section)
Notes to Section 4
5. Axial circular transformations
A. Dilatation
B. Axial inversion
Notes to Section 5
Supplement I
Non-euclidean geometry of Lobachevskii-Bolyai, or hyperbolic geometry
Notes to Supplement I
Solutions
Section 1
Section 2
Section 3
Circular transformations
Section 4
Section 5
Supplement II
Notes to Supplement II.
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