Abstract

Let S2\mathbb{S}^2 be the unit sphere in R3\mathbb{R}^3 and let C⊂S2C\subset \mathbb{S}^2 be a spherical convex body of constant width τ\tau. It is known that
(i) if τ<π/2\tau<\pi/2 then for any ε>0\varepsilon>0 there exists a spherical convex body CεC_\varepsilon of constant width τ\tau whose boundary consists only of arcs of circles of radius τ\tau such that the Hausdorff distance between CC and CεC_\varepsilon is at most ε\varepsilon;
(ii) if τ>π/2\tau>\pi/2 then for any ε>0\varepsilon>0 there exists a spherical convex body CεC_\varepsilon of constant width τ\tau whose boundary consists only of arcs of circles of radius τ−π2\tau-\frac{\pi}{2} and great circle arcs such that the Hausdorff distance between CC and CεC_\varepsilon is at most ε\varepsilon.
In this paper, we present an approximation of the remaining case τ=π/2\tau=\pi/2, that is, if τ=π/2\tau=\pi/2 then for any ε>0\varepsilon>0 there exists a spherical polygon Pε\mathcal{P}_\varepsilon of constant width π/2\pi/2 such that the Hausdorff distance between CC and Pε\mathcal{P}_\varepsilon is at most ε\varepsilon.

Author information

Contact details are reproduced from the original publication and may be historical.

Huhe Han

College of Science, Northwest Agriculture and Forestry University, Xianyang, Shaanxi, China

han-huhe@nwafu.edu.cn

Keywords

  • Constant width
  • approximation
  • spherical polytgon
  • Hausdorff distance

Mathematics Subject Classification

52A55

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Suggested citation

H. Han. “Approximation of Spherical Convex Bodies of Constant Width π/2.” Journal of Convex Analysis 33 (2026), No. 1&2, 415–420. https://doi.org/10.68381/jca33025

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Published by Heldermann Verlag, 2026. Rights now held by Banach Press.