Approximation of Spherical Bodies of Constant Width and Reduced Bodies

Marek Lassak

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arXiv · 2106.00118

Approximation of Spherical Bodies of Constant Width and Reduced Bodies

Marek Lassak

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Abstract

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

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Marek Lassak. 2021-05-31. Approximation of Spherical Bodies of Constant Width and Reduced Bodies. https://arxiv.org/abs/2106.00118

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