Differential Geometry of Plane Curves
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A01=Gregorio Silva Neto
A01=Hilario Alencar
A01=Walcy Santos
Author_Gregorio Silva Neto
Author_Hilario Alencar
Author_Walcy Santos
Category=PBM
Category=PBP
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eq_isMigrated=2
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Product details
- ISBN 9781470469597
- Weight: 512g
- Dimensions: 140 x 216mm
- Publication Date: 30 Jul 2022
- Publisher: American Mathematical Society
- Publication City/Country: US
- Product Form: Paperback
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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.
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.
Hilario Alencar, Federal University of Alagoas, Maceio, Alagoas, Brazil.
Walcy Santos, Federal University of Rio de Janeiro, Brazil.
Gregorio Silva Neto, Universidade Federal de Alagoas, Maceio, Alagoas, Brazil.
Walcy Santos, Federal University of Rio de Janeiro, Brazil.
Gregorio Silva Neto, Universidade Federal de Alagoas, Maceio, Alagoas, Brazil.
