A system of points on a sphere S of radius R “induces” on the sphere S0 of radius R0 three different sets of points, which are geometric medians (GM) -local maxima, minima and saddle points sum of distance function f(x). The angular coordinates of the spherical distribution of a system of points - local minima coincide with the original system of points.
Distribution of points Pi, test Point, Max/min/saddle -Critical points on a sphere. Vectors ∇f and ∇g at these points.
![[size=85]A system of points on a sphere S of radius R “induces” on the sphere S0 of radius R0 three different sets of points, which are [color=#93c47d]geometric medians (GM)[/color] -local [color=#ff0000]maxima[/color], [color=#6d9eeb]minima[/color] and [color=#38761d]saddle[/color] points sum of distance function f(x). The angular coordinates of the spherical distribution of a system of points -[color=#0000ff] local minima[/color] coincide with the original system of points.[/size]](https://www.geogebra.org/resource/bbkb3h3u/SXX42lohIp4uo4XS/material-bbkb3h3u.png)
![Distribution of points P[sub]i, [/sub][color=#5b0f00]test Point[/color][sub], [/sub] [color=#ff0000]Max[/color]/[color=#0000ff]min[/color]/[color=#38761d]saddle[/color] -[color=#333333]Critical points[/color] on a sphere. Vectors ∇f and ∇g at these points.](https://www.geogebra.org/resource/fbvxtuqn/nKhrJxB3ae8oW3BV/material-fbvxtuqn.png)
![[color=#ff0000]max:[/color] Gyroelongated square bipyramid [color=#0000ff]min:[/color] Anticube [color=#6aa84f]sad:[/color] Octagonal Antiprism](https://www.geogebra.org/resource/edcre6e4/dzSusndF2bIdMpcq/material-edcre6e4.png)
