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A Differential Approach to GeometryPlane Curves

A Differential Approach to Geometry: Plane Curves [Plane curves are studied both via their parametric equations or their Cartesian equation. We study the tangent to a curve and the related problem of the envelope of a family of curves; we exhibit some interesting applications in physics. After a careful study of the curvature of a plane curve, its intrinsic equation and the famous Umlaufsatz, we switch to the more involved question of simple closed and convex curves and we prove in particular the Hopf and the “Four vertices” theorems.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A Differential Approach to GeometryPlane Curves

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/lp/springer-journals/a-differential-approach-to-geometry-plane-curves-V8aB0b0BK0
Publisher
Springer International Publishing
Copyright
© Springer International Publishing Switzerland 2014
ISBN
978-3-319-01735-8
Pages
55 –138
DOI
10.1007/978-3-319-01736-5_2
Publisher site
See Chapter on Publisher Site

Abstract

[Plane curves are studied both via their parametric equations or their Cartesian equation. We study the tangent to a curve and the related problem of the envelope of a family of curves; we exhibit some interesting applications in physics. After a careful study of the curvature of a plane curve, its intrinsic equation and the famous Umlaufsatz, we switch to the more involved question of simple closed and convex curves and we prove in particular the Hopf and the “Four vertices” theorems.]

Published: Aug 26, 2013

Keywords: Rotation Number; Plane Curve; Normal Representation; Parametric Representation; Plane Curf

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