# ₊Finding the optimal relative position of the" repulsive " set of particles on the sphere

- Author:
- Roman Chijner

**Generating a uniform distribution of points on a sphere.**Let S be a sphere of radius R around the point O: S:={x∈ℝ^{³}: ||x||=R}.*There is a set lP={A1, A2,...,An}*of**.**__n movable free points on a sphere__**Problem**: use the**find such their distribution corresponding to the***method of Lagrange multipliers***maximum****sum of all their mutual distances**.*This means need to find out such**mutual arrangement*of "*when each point of this set is**repulsive" set of*__particles on a sphere__,*of the remaining n-1 points.***Geometric median**(**GM)***We assume that the equilibrium -**stationary state**in system of "charges" is reached if the sum of their mutual distances is maximal.**of**Iterative approach**is applied for**particle placement**achieving**a stationary state.**An*iterative procedure

*for calculating a polyhedron with an extreme vertex arrangement allows one point to be fixed at any point on the sphere. In the applet, point A can be set at any point in the sphere. For orientation, you can set Check box "*sphere

*" - true. Click on the "*

**Click→Input,Initial settings**

*"-button and other starting points will be randomly set. Click the "*Start

*"-button and wait for the iteration process to finish! Note: 1.Theoretical instructions can be found in https://www.geogebra.org/m/rcm4ayek 2.Images and explanations to them in https://www.geogebra.org/m/uegb5ym3 3.This applet might not work properly in the online worksheet, but it works well in a ggb file. *old*version