Differential Geometry of Plane Curves

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Mathematics - Geometry and Topology
Differential Geometry of Plane Curves

Differential Geometry of Plane Curves

Name: Differential Geometry of Plane Curves
ISBN: 9781470469597

Hilário Alencar, Walcy Santos, Gregório Silva Neto

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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.

Categorías:

Mathematics - Geometry and Topology

Volumen:

Año:

2022

Edición:

Editorial:

American Mathematical Society

Idioma:

english

Páginas:

416