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Plane Curves

In: A Differential Approach to Geometry

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Listed:
  • Francis Borceux

    (Université catholique de Louvain)

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.

Suggested Citation

  • Francis Borceux, 2014. "Plane Curves," Springer Books, in: A Differential Approach to Geometry, edition 127, chapter 0, pages 55-138, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-01736-5_2
    DOI: 10.1007/978-3-319-01736-5_2
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