On the closed planar homothetic motions and the orbital areas

Abstract

In this study, it is shown th a t ali the fixed points of the moving plane each. of which has equal orbital areas in the fixed plane under the I-param eter closed planar hom othetic m otion lie on the same circle in th e moving plane the çenter of w hich is generally different from the Steiner point. For the closed planar hom othetic m otions, obtaining a foram la which is analogue of H oditch form ula some corollarics are found.