Holditch Theorem and Steiner Formula for the Planar Hyperbolic Motions

Abstract

The Steiner formula and the Holditch Theorem for one-parameter closed planar Euclidean motions [1, 7] were expressed by H.R. Muller [9] under the one-parameter closed planar motions in the complex sense. In this paper, in analogy with complex motions as given by Muller [9], the Steiner formula and the mixture area formula are obtained under one parameter hyperbolic motions. Also Holditch theorems were expressed in the hyperbolic sense.