Geometry of Chain of Spheres Inside an Ellipsoidal Fragment.

The objective of this article is to establish a condition by which we are able to state that an ellipsoidal fragment formed by a plane cutting the ellipsoid can always contain a sphere in any position inside in it. A method to construct a chain of mutually tangent spheres inscribed in the ellipsoidal segment has been proposed. The locus of the centroid as well as the radii of the mutually tangent spheres have been computed. The prime concern of our work is to explore some geometrical properties of such a chain of spheres which includes the condition of inscribability of a sphere in any position inside the ellipsoid along with the computation of points of tangency between consecutive spheres. [ABSTRACT FROM AUTHOR]