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Differential Geometry of Plane Curves (Paperback)
Loot Price: R1,545
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Differential Geometry of Plane Curves (Paperback)
Series: Student Mathematical Library
Expected to ship within 12 - 17 working days
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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.
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