On the Number of Spherical Circles Needed to Cover a Spherical Convex Domain - Elad Atia; Reuven Cohen; Shai Gul (Mathematics)
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.