Geometric Transformations: Volume 4, Circular Transformations: 44 (Anneli Lax New Mathematical Library, Series Number 44) - Softcover

Yaglom, I. M.

Softcover

ISBN 10: 0883856484 ISBN 13: 9780883856482

Publisher: The Mathematical Association of America, 2009

Synopsis

A comprehensive treatment of the geometry of circular transformations.

About this title

About the Authors

I. M. Yaglom authored many books which have since become academic standards of reference. These include Complex Numbers in Geometry, Geometric Transformations, A Simple Non-Euclidean Geometry and its Physical Basis, and Probability and Information. He was Professor of Mathematics at Yaroslavl State University from 1974–83 and a technical consultant at the Academy of Pedagogical Sciences from 1984–88.

Abe Shenitzer has translated many mathematics classics (from German, Polish and Russian into English). He retired in 1989 from York University, where he had been Professor of Mathematics since 1969.

From the Back Cover

The familiar plane geometry of high 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, which appeared in this series as Volumes 8, 21, and 24. Part I treats the geometry of rigid motions of the plane (isometries); Part II treats the geometry of shape-preserving transformations of the plane (similarities); Part III treats the geometry of transformations of the plane that map lines to lines (affine and projective transformations) and introduces the Klein model of non-Euclidean geometry. 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 high-school geometry and trigonometry. 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.

Edition details

• Publisher: The Mathematical Association of America
• Publication date: 2009
• Language: English
• ISBN 10: 0883856484
• ISBN 13: 9780883856482
• Binding: Paperback
• Number of pages: 293