Despite the geometric median's being an easy-to-understand concept, computing it poses a challenge. The centroid or center of mass, defined similarly to the geometric median as minimizing the sum of the "squares" of the distances to each point, can be found by a simple formula — its coordinates are the averages of the coordinates of the points — but it has been shown that no explicit formula, nor an exact algorithm involving only arithmetic operations and "k"th roots, can exist in general for the geometric median. Therefore, only numerical or symbolic approximations to the solution of this problem are possible under this model of computation.