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

- Author:
- Roman Chijner

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(*, some way distributed in space. The**f**_{q}-function of the sum of squares of all distances)*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**and you can***exact solution**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/f**on a circle is "working". Move the test point_{q}**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.*