Example of non-uniqueness of the extreme distribution of n=16 particles on the surface of a sphere.
- Roman Chijner
- Vectors 2D (Two-Dimensional), Vectors 3D (Three-Dimensional), Arithmetic Mean, Centroid or Barycenter, Combinatorics, Coordinates, Equilateral Triangles, Optimization Problems, Geometric Mean, Geometry, Isosceles Triangles, Linear Programming or Linear Optimization, Mathematics, Means, Planes, Polygons, Solids or 3D Shapes, Special Points, Sphere, Surface, Geometric Transformations, Volume
The number of particles on the surface of the sphere is the same. They are placed according to the maximum Distance Sum principle. The "measure" of this distribution is the p-average distance between these particles on the unit sphere. Here, using the example n=16, it is shown, that there are at least two such extreme distributions: p1 = 1.408 486 535 365 533; p2 = 1.408 492 668 681 228. These two distributions are obtained here by a different choice of initial settings-distributions for a further iterative procedure.