This book features plane curves-the simplest objects in differential geometry-to illustrate many deep and inspiring results in the field in an elementary and accessible way. After an introduction to the basic properties of plane curves, the authors introduce a number of complex and beautiful topics, including the rotation number (with a proof of the fundamental theorem of algebra), rotation index, Jordan curve theorem, isoperimetric inequality, convex curves, curves of constant width, and the four-vertex theorem. The last chapter connects the classical with the modern by giving an introduction to the curve-shortening flow that is based on original articles but requires a minimum of previous knowledge.
Over 200 figures and more than 100 exercises illustrate the beauty of plane curves and test the reader's skills. Prerequisites are courses in standard one variable calculus and analytic geometry on the plane.
| ISBN: | 9781470469597 |
| Publication date: | 30th July 2022 |
| Author: | Hilário Alencar |
| Publisher: | American Mathematical Society |
| Format: | Paperback |
| Pagination: | 416 pages |
| Series: | Student Mathematical Library |
| Genres: |
Geometry Topology |
This book features plane curves-the simplest objects in differential geometry-to illustrate many deep and inspiring results in the field in an elementary and accessible way. After an introduction to the basic properties of plane curves, the authors introduce a number of complex and beautiful topics, including the rotation number (with a proof of the fundamental theorem of algebra), rotation index, Jordan curve theorem, isoperimetric inequality, convex curves, curves of constant width, and the four-vertex theorem. The last chapter connects the classical with the modern by giving an introduction to the curve-shortening flow that is based on original articles but requires a minimum of previous knowledge.
Over 200 figures and more than 100 exercises illustrate the beauty of plane curves and test the reader's skills. Prerequisites are courses in standard one variable calculus and analytic geometry on the plane.
Differential Geometry of Plane Curves features in the following genres: Geometry, Topology
Differential Geometry of Plane Curves is available in Paperback
Differential Geometry of Plane Curves was written by Hilário Alencar and published by American Mathematical Society
Differential Geometry of Plane Curves has 416 pages
Yes it is part of Student Mathematical Library series