Optimizing the Arrangement of Points on the Unit Sphere

DOI10.2307/2006132zbMath0379.90112OpenAlexW4247062390MaRDI QIDQ4158853

K. Hanes, Joel D. Berman

Publication date: 1977

Full work available at URL: https://doi.org/10.2307/2006132

Mathematics Subject Classification ID

Mathematical programming (90C99)

Related Items (10)

Local diameters of compact planar sets ⋮ Approximating spheres and sphere patches ⋮ Local critical analysis of inequalities related to the sum of distances between \(n\) points on the unit hemisphere for \(n=4,5\) ⋮ Problems, problems, problems ⋮ On improved bounds for bounded degree spanning trees for points in arbitrary dimension ⋮ Optimal \(N\)-point configurations on the sphere: ``magic numbers and Smale's 7th problem ⋮ Spherical distribution of 5 points with maximal distance sum ⋮ Hilbert's `monkey saddle' and other curiosities in the equilibrium problem of three point particles on a circle for repulsive power law forces ⋮ Upper bounds for Kruskal's stress ⋮ A mechanical method for isolating locally optimal points of certain radical functions

Cites Work

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• The sum of the distances to N points on a sphere
• Volumes of polyhedra inscribed in the unit sphere in \(E^3\)
• On the sum of distances determined by a pointset
• Stability Configurations of Electrons on a Sphere
• Extremal Problems of Distance Geometry Related to Energy Integrals
• Inequalities for Sums of Distances
• Sums of Distances Between Points on a Sphere. II
• Some geometric extremal problems
• On the sum of distances betweenn points on a sphere
• Search for Largest Polyhedra

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