TRANSFORMATION GEOMETRY: Translation, Reflection, Rotation, Dilation in plane and in 3-dimensional Euclidean space - Softcover

MISRA, RAM BILAS

Softcover

ISBN 10: 384338827X ISBN 13: 9783843388276

Publisher: LAP LAMBERT Academic Publishing, 2010

Synopsis

The first chapter deals with the transformations (more precisely translation, reflection, rotation, dilation) in a plane while similar transformations in a 3-dimensional Euclidean space are dealt with in the second chapter. Non-linear, affine and locally affine transformations and rigid motions are included. Isometries are introduced in the third chapter. Chapter 4 offers a detailed account of product transformations which form an algebraic group. Infinitesimal transformations are introduced in Chapter 5. Cases when they may form a motion (preserving distances), translation (displacing each point through a fixed distance), conformal motion (preserving the angle between two directions), homothetic motion (a special case of conformal motion) and geodesic preserving transformations (called projective motions) are dealt therein. The last chapter defines a projective space in general and projective transformations: both singular and non-singular are studied. The chapter concludes with the projective transformations of a projective space onto itself, called collineations. Certain properties of collineations are studied.

About this title

About the Author

Prof Dr RB Misra has been teaching Maths at UG/PG levels since 1962. Starting from the Uni of Allahabad (4th oldest Uni in the Indian sub-continent) he taught at various universities within India and abroad.He published over 150 Res. Articles in Maths in leading journals of international repute and has been a regular Reviewer in MR and Zbl.

Edition details

• Publisher: LAP LAMBERT Academic Publishing
• Publication date: 2010
• Language: English
• ISBN 10: 384338827X
• ISBN 13: 9783843388276
• Binding: Paperback
• Number of pages: 88