The areas of the trajectory surface under the Galilean motions in the Galilean space

Abstract

In the literature, Holditch theorem was obtained under periodic rotation and translation motions in [H. Holditch, Geometrical theorem, Q. J. Pure Appl. Math. 2 (1858) 38] or periodic shear and translation motions in [O. Roschel, Der satz von Holditch in der isotropen ebene. Abh. Braunschweig. Wiss. Ges. 36 (1984) 27-32]. In this paper, by introducing the projection of a vector onto a plane, scalar area, area vector of a surface, we investigate Holditch theorem under periodic rotation, translation and shear motions. We give two interpretations for the Holditch type theorem in Galilean space.