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A Note on the Torsion of Bernstein Curves

Published online by Cambridge University Press:  20 November 2018

Martin E. Price
Martin E. Price*
Affiliation:
Framingham State College, Framingham, MA 01701
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Abstract

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It is shown that Bernstein Polynomials do not diminish the total “twist” of space curves in contrast to their length and curvature diminishing properties. This phenomenon is shown to be related to the fact that Bernstein Polynomials of a plane curve may have more inflections than the curve possesses.

Keywords

41A10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 3 , 01 September 1984 , pp. 257 - 259
Copyright
Copyright © Canadian Mathematical Society 1984

References

1. Fary, I., Sur certaines inégalités géométriques, Acta Szeged (1950), pp. 117–124.Google Scholar
2. Lorentz, G., Bernstein polynomials, University of Toronto Press (1953).Google Scholar
3. Price, M., The Bend of Bernstein polynomials, Aequationes Mathematicae (1974), pp. 138–141.Google Scholar
4. Schoenberg, I. J., Variation diminishing approximation methods (from “On Numerical Approximation”), University of Wisconsin (1959), pp. 249–274.Google Scholar