The Centroid As A Subtle Attractor of The Geometric Median As The Number of Points In A Set Enlarges, On The Web

A central point, termed the "geometric median", for a set of points in a plane, is computed by the minimization of the sum of the distances to all the points in the set, randomly placed (or given). Our question is to assess the proximity between that central point and the centroid, i.e., to observe the distance between them as the number of points in the set (its cardinality) enlarges. The minimization of the sum is performed by the classic Weiszfeld algorithm, and optionally by other common methods (from Python scipy.optimize.minimize). Our study shows that this distance becomes insignificant, as verifiable in this text, for a large cardinality in the set, a situation where the computing time would become excessive. A web page is given to make the computing freely available and trustworthy.