Translated by A. Shenitzer.
Softcover ISBN:  9780883856482 
Product Code:  NML/44 
List Price:  $65.00 
MAA Member Price:  $48.75 
AMS Member Price:  $48.75 
eBook ISBN:  9780883859582 
Product Code:  NML/44.E 
List Price:  $50.00 
MAA Member Price:  $37.50 
AMS Member Price:  $37.50 
Softcover ISBN:  9780883856482 
eBook: ISBN:  9780883859582 
Product Code:  NML/44.B 
List Price:  $115.00 $90.00 
MAA Member Price:  $86.25 $67.50 
AMS Member Price:  $86.25 $67.50 
Translated by A. Shenitzer.
Softcover ISBN:  9780883856482 
Product Code:  NML/44 
List Price:  $65.00 
MAA Member Price:  $48.75 
AMS Member Price:  $48.75 
eBook ISBN:  9780883859582 
Product Code:  NML/44.E 
List Price:  $50.00 
MAA Member Price:  $37.50 
AMS Member Price:  $37.50 
Softcover ISBN:  9780883856482 
eBook ISBN:  9780883859582 
Product Code:  NML/44.B 
List Price:  $115.00 $90.00 
MAA Member Price:  $86.25 $67.50 
AMS Member Price:  $86.25 $67.50 

Book DetailsAnneli Lax New Mathematical LibraryVolume: 44; 2009; 285 pp
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 shapepreserving 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 nonEuclidean 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 rulerandcompass constructions and the Poincaré model of hyperbolic geometry. The straightforward, direct presentation assumes only some background in highschool 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.

Table of Contents

Chapters

Chapter 1. Reflection in a circle (inversion)

Chapter 2. Application of inversions to the solution of constructions

Chapter 3. Pencils of circles. The radical axis of two circles

Chapter 4. Inversion (concluding section)

Chapter 5. Axial circular transformations

Supplement

Solutions


Additional Material

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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 shapepreserving 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 nonEuclidean 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 rulerandcompass constructions and the Poincaré model of hyperbolic geometry. The straightforward, direct presentation assumes only some background in highschool 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.

Chapters

Chapter 1. Reflection in a circle (inversion)

Chapter 2. Application of inversions to the solution of constructions

Chapter 3. Pencils of circles. The radical axis of two circles

Chapter 4. Inversion (concluding section)

Chapter 5. Axial circular transformations

Supplement

Solutions