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, 5] were expressed by Muller, under the one-parameter closed planar motions in the complex sense. Also, Muller had given Holditch theorem in the complex sense, [6]. In this paper, in analogy with Complex motions as given by Muller [6], the Steiner formula and the mixture area formula are obtained under one parameter hyperbolic motions. Also Holditch theorem was expressed in the hyperbolic sense.