Format:
1 Online-Ressource(XV, 231 Seiten)
,
Illustrationen
ISBN:
9783031250026
Series Statement:
Undergraduate Texts in Mathematics
Content:
Motivation -- I Euclidean and Inversive Geometry -- Euclidean Isometries and Similarities -- Inversive Geometry -- Applications of Inversive Geometry -- II Non-Euclidean Geometry -- Spherical Geometry -- Appendix: Set Theory.
Content:
The principle aim of this unique text is to illuminate the beauty of the subject both with abstractions like proofs and mathematical text, and with visuals, such as abundant illustrations and diagrams. With few mathematical prerequisites, geometry is presented through the lens of linear fractional transformations. The exposition is motivational and the well-placed examples and exercises give students ample opportunity to pause and digest the material. The subject builds from the fundamentals of Euclidean geometry, to inversive geometry, and, finally, to hyperbolic geometry at the end. Throughout, the author aims to express the underlying philosophy behind the definitions and mathematical reasoning. This text may be used as primary for an undergraduate geometry course or a freshman seminar in geometry, or as supplemental to instructors in their undergraduate courses in complex analysis, algebra, and number theory. There are elective courses that bring together seemingly disparate topics and this text would be a welcome accompaniment.
Additional Edition:
ISBN 9783031250019
Additional Edition:
ISBN 9783031250033
Additional Edition:
ISBN 9783031250040
Additional Edition:
Erscheint auch als Druck-Ausgabe Sheydvasser, Arseniy Linear fractional transformations Cham, Switzerland : Springer, 2023 ISBN 9783031250019
Additional Edition:
ISBN 303125001X
Additional Edition:
ISBN 9783031250040
Language:
English
DOI:
10.1007/978-3-031-25002-6
