On the volume of the trajectory surfaces under the homothetic motions

DÜLDÜL M., KURUOĞLU N.

Acta Mathematica Universitatis Comenianae, vol.76, no.2, pp.241-246, 2007 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 76 Issue: 2
  • Publication Date: 2007
  • Journal Name: Acta Mathematica Universitatis Comenianae
  • Journal Indexes: Scopus
  • Page Numbers: pp.241-246
  • Keywords: Holditch theorem, Homothetic motion, Volume of trajectory surface
  • Istanbul Gelisim University Affiliated: Yes

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.