Searching for the Centers of Spheres and Ellipsoids

Biedl first posed the problem of finding the center of a circle, starting from a point on the boundary and using a limited number of operations. They presented an open problem for searching the center of an ellipse in their paper. Later, Burr solved that problem. However, in both of their works, they considered the searching space to be two dimensional. As a result, their strategies do well on a plane but in reality the searching space is three dimensional in most of the cases. In those cases we need an efficient strategy to find out the center of a sphere or in some cases, the center of an ellipsoid. In this paper, we have proposed different strategies for finding the centers of spheres and ellipsoids.