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      Chapter

      Plane Curves: Global Properties
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      Chapter

      Plane Curves: Global Properties

      DOI link for Plane Curves: Global Properties

      Plane Curves: Global Properties book

      Plane Curves: Global Properties

      DOI link for Plane Curves: Global Properties

      Plane Curves: Global Properties book

      ByThomas Banchoff, Stephen Lovett
      BookDifferential Geometry of Curves and Surfaces

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      Edition 2nd Edition
      First Published 2015
      Imprint Chapman and Hall/CRC
      Pages 24
      eBook ISBN 9780429156229
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      ABSTRACT

      Global properties concern attributes about the curve taken as a whole. The tangential indicatrix of a curve lies entirely on the unit circle in the plane but with possibly a complicated parametrization. The winding number of a regular curve around a point offers a strategy to prove the Jordan Curve Theorem in the case when the curve is regular. The concept of a vertex is obviously a local property of the curve, but if one were to experiment with a variety of closed curves, one would soon guess that there must be a restriction on the number of vertices. Isoperimetric inequality is an example of a global theorem since it relates quantities that take into account the entire curve at once.

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