On the volume of the trajectory surfaces under the homothetic motions

Abstract

The volumes of the surfaces of 3-dimensional Euclidean Space which are traced by a fixed point as a trajectory surface during 3-parametric motions are given by H. R. Müller [3], [4], [5] and W. Blaschke [1]. In this paper, the volumes of the trajectory surfaces of fixed points under 3-parametric homothetic motions are computed. Also, using a certain pseudo-Euclidean metric we generalized the well-known classical Holditch Theorem, [2], to the trajectory surfaces. © 2008 Elsevier B.V., All rights reserved.