| Introduction to Classical Geometries 2007 Edition Contributor(s): Ramírez Galarza, Ana Irene (Author), Seade, José (Author) |
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ISBN: 3764375175 ISBN-13: 9783764375171 Publisher: Birkhauser OUR PRICE: $52.24 Product Type: Paperback - Other Formats Published: March 2007 Annotation: This book follows Kleins proposal of studying geometry by looking at the symmetries (or rigid motions) of the space in question. In this way the classical geometries are studied: Euclidean, affine, elliptic, projective and hyperbolic. For simplicity the focus is on the two-dimensional case, which is already rich enough, though some aspects of the 3 or $n$-dimensional geometries are included. Once plane geometry is well understood, it is much easier to go into higher dimensions. The book appeals to, and develops, the geometric intuition of the reader. Some basic notions of algebra and analysis are also used to get better understandings of various concepts and results. |
| Additional Information |
| BISAC Categories: - Mathematics | Geometry - General |
| Dewey: 516 |
| Physical Information: 0.49" H x 6.8" W x 9.41" (1.01 lbs) 220 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: Geometry is one of the oldest branches of mathematics, nearly as old as human culture.Itsbeautyhasalwaysfascinatedmathematicians, amongothers.Inwriting this book we had the purpose of sharing with readers the pleasure derived from studying geometry, as well as giving a tasteof its importance, its deep connections with other branches of mathematics and the highly diverse viewpoints that may be taken by someone entering this ?eld. We also want to propose a speci?c way to introduce concepts that have arisen from the heyday of the Greek school of geometry to the present day. We workwithcoordinatemodels, sincethis facilitatestheuseofalgebraicandanalytic results, and we follow the viewpoint proposed by Felix Klein in the 19th century, of studying geometry via groups of symmetries of the space in question. We intend this book to be both an introduction to the subject addressed to undergraduate students in mathematics and physics, and a useful text-book for mathematicians and scientists in general who want to learn the basics of classical geometry: Euclidean, a?ne, elliptic, hyperbolic and projective geometry. These are all presented in a uni?ed way and the essential content of this book may be covered in a single semester, though a longer period of study would allow the student to grasp and assimilate better the material in |