| Softcover ISBN: | 978-1-4704-6959-7 |
| Product Code: | STML/96 |
| List Price: | $59.00 |
| Individual Price: | $47.20 |
| eBook ISBN: | 978-1-4704-7036-4 |
| Product Code: | STML/96.E |
| List Price: | $59.00 |
| Individual Price: | $47.20 |
| Softcover ISBN: | 978-1-4704-6959-7 |
| eBook: ISBN: | 978-1-4704-7036-4 |
| Product Code: | STML/96.B |
| List Price: | $118.00 $88.50 |
| Softcover ISBN: | 978-1-4704-6959-7 |
| Product Code: | STML/96 |
| List Price: | $59.00 |
| Individual Price: | $47.20 |
| eBook ISBN: | 978-1-4704-7036-4 |
| Product Code: | STML/96.E |
| List Price: | $59.00 |
| Individual Price: | $47.20 |
| Softcover ISBN: | 978-1-4704-6959-7 |
| eBook ISBN: | 978-1-4704-7036-4 |
| Product Code: | STML/96.B |
| List Price: | $118.00 $88.50 |
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Book DetailsStudent Mathematical LibraryVolume: 96; 2022; 416 ppMSC: Primary 53
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.
ReadershipUndergraduate and graduate students interested in curves in the Euclidean plane.
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Table of Contents
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Chapters
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Plane curves
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Winding number
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Rotation index
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Jordan curve theorem
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Isoperimetric inequality
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Convex curves
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The four-vertex theorem
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Curve-shortening flow
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Appendix A. The class $\mathcal {C}^\infty $ convergence of the curvature function under the curve-shortening flow
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Appendix B. Answers to selected exercises
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Additional Material
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Reviews
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The authors focus their attention on the differential geometry of planar curves with great depth, although phenomenal books on differential geometry already exist. Many interesting and inspiring geometrical and topological results on planar curves are here presented in an elementary form. The topics are chosen to sharpen the reader's mathematical intuition for asserted geometric concepts and results. A very good selection of examples guides the reader towards a better understanding of each notion.
Ergin Bayram (Samsun)
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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
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.
Undergraduate and graduate students interested in curves in the Euclidean plane.
-
Chapters
-
Plane curves
-
Winding number
-
Rotation index
-
Jordan curve theorem
-
Isoperimetric inequality
-
Convex curves
-
The four-vertex theorem
-
Curve-shortening flow
-
Appendix A. The class $\mathcal {C}^\infty $ convergence of the curvature function under the curve-shortening flow
-
Appendix B. Answers to selected exercises
-
The authors focus their attention on the differential geometry of planar curves with great depth, although phenomenal books on differential geometry already exist. Many interesting and inspiring geometrical and topological results on planar curves are here presented in an elementary form. The topics are chosen to sharpen the reader's mathematical intuition for asserted geometric concepts and results. A very good selection of examples guides the reader towards a better understanding of each notion.
Ergin Bayram (Samsun)
