On the Number of Spherical Circles Needed to Cover a Spherical Convex Domain

Elad Atia, Reuven Cohen () and Shai Gul
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Elad Atia: Computer Science Department, College of Management Academic Studies, Rishon LeZion 75490, Israel
Reuven Cohen: Department of Mathematics, Bar-Ilan University, Ramat-Gan 5290002, Israel
Shai Gul: Department of Mathematics, Holon Institute of Technology, Holon 5810201, Israel

Mathematics, 2025, vol. 13, issue 15, 1-13

Abstract: In this manuscript, we study the coverage of convex spherical domains by spherical circles. This question can be applied to the location of satellites, weather balloons, radio towers, etc. We present an upper bound on the number of spherical circles of radius r needed to cover a spherical convex domain K , in terms of the respective area and perimeter. Then, we calculate the asymptotic density of such cover, when the radius approaches zero.

Keywords: integral geometry; spherical convex domains; spherical covering (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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