[size=85] 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 [color=#ff0000]extrema[/color] -[i][color=#ff0000]located on a circle[/color][/i], of the [b][color=#1e84cc]f[/color][/b]-[i]function of the [color=#1e84cc]sum of all distances[/color] of a system of n points([b][color=#ff00ff]f[/color][/b][sub][color=#ff00ff]q[/color][/sub]-function of the sum of squares of all distances)[/i], some way distributed in space. The [i]method of Lagrange multipliers[/i] is used to find the [color=#ff0000]extrema[/color] of the function [b]f[/b] subject to [i]constraints[/i] - [color=#ff0000]extrema[/color] should be located [i]on the circle[/i]. By choosing the [color=#f1c232]test points[/color] for the iterative procedure, various solutions can be found. [br] This problem has an [b][i]exact solution[/i][/b] and you can [i]compare[/i] the exact results and the results of the iterative approximate method. On its basis, one can make sure that the iterative procedure of the [i]method of Lagrange Multipliers[/i] to find the [color=#ff0000]extreme[/color] points оf [b][color=#1e84cc]f[/color]/[color=#ff00ff]f[/color][sub][color=#ff00ff]q[/color][/sub][/b] on a circle is "working".[br] Move the test point [b][color=#9900ff]po[/color][/b] and observe the corresponding [i]multiple[/i] solutions: the locations of [i][color=#ff7700]Geometric medians/[/color][color=#ff00ff]Geometric centers[/color][/i].[br][sup]*[/sup]From [url=https://www.geogebra.org/m/u7zq6f3e]Book[/url]: ΛM 2d: Location estimators on a circle for a set of points. ΛM -[i]method of Lagrange multipliers.[/i][/size]