Four points [color=#ff0000]A[/color], B, C, D are taken at random on a sphere of radius r (use θ and φ reglers). The volume of the tetrahedron ABCD is greatest in the case of its regularity. Point [color=#ff0000]A[/color] moves freely around the sphere.[br] Using geogebra this problem is solved by computing the maxima of functions of 6 variables.