3D. Explanation of Invariance of the sum of squares of distances by using the Steiner theorem.
- Author:
- Roman Chijner
n/2 points of A1,...,An may be moving on the surface of a sphere of radius r. Each point has antipodal point on a sphere . Thus, the center of gravity is the centre of the sphere.
It is shown, that the sum of squares of distances from any point D of a sphere to →{Ai} , divided by radius squared, is always equal of twice the number of points.
https://en.wikipedia.org/wiki/Parallel_axis_theorem
https://en.wikipedia.org/wiki/Antipodal_point