Abstract

We present a spherical version of the theorem of Blaschke that every body of constant width w < π/2 can be approximated by a body of constant width w whose boundary consists only of pieces of circles of radius w as well as we wish in the sense of the Hausdorff distance. This is a special case of our theorem about approximation of spherical reduced bodies.

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Keywords

  • Sphere
  • spherical convex body
  • body of constant width
  • reduced body
  • Hausdorff distance
  • approximation

Mathematics Subject Classification

52A55

References

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Suggested citation

M. Lassak. “Approximation of Spherical Bodies of Constant Width and Reduced Bodies.” Journal of Convex Analysis 29 (2022), No. 3, 921–928. https://doi.org/10.68381/jca29052

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Published by Heldermann Verlag, 2022. Rights now held by Banach Press LLC.