Finding the location of geometric medians/centers on the circle from discrete sample points depending on the position of the test point.

An example of the problem of distribution of "extreme points" on a circle ("called", "guided", "induced") by a system of n points. You can use the applet to explore the distribution of positions of the extrema -located on a circle, of the f-function of the sum of all distances of a system of n points(fq-function of the sum of squares of all distances), some way distributed in space. The method of Lagrange multipliers is used to find the extrema of the function f subject to constraints - extrema should be located on the circle. By choosing the test points for the iterative procedure, various solutions can be found. This problem has an exact solution and you can compare the exact results and the results of the iterative approximate method. On its basis, one can make sure that the iterative procedure of the method of Lagrange Multipliers to find the extreme points оf f/fq on a circle is "working". Move the test point po and observe the corresponding multiple solutions: the locations of Geometric medians/Geometric centers. *From Book: ΛM 2d: Location estimators on a circle for a set of points. ΛM -method of Lagrange multipliers.