Plane Curves

Francis Borceux
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Francis Borceux: Université catholique de Louvain

Chapter Chapter 2 in A Differential Approach to Geometry, 2014, pp 55-138 from Springer

Abstract: 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.

Keywords: Rotation Number; Plane Curve; Normal Representation; Parametric Representation; Plane Curf (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-01736-5_2

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DOI: 10.1007/978-3-319-01736-5_2

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