Holditch theorem and Steiner formula for the planar hyperbolic motions

YÜCE S., KURUOĞLU N.

Advances in Applied Clifford Algebras, vol.19, no.1, pp.155-160, 2009 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 19 Issue: 1
  • Publication Date: 2009
  • Doi Number: 10.1007/s00006-008-0131-6
  • Journal Name: Advances in Applied Clifford Algebras
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.155-160
  • Keywords: Holditch Theorem, Hyperbolic motion, Hyperbolic numbers
  • Istanbul Gelisim University Affiliated: Yes

Abstract

The Steiner formula and the Holditch Theorem for one-parameter closed planar Euclidean motions [1, 7] were expressed by H.R. Müller [9] under the one-parameter closed planar motions in the complex sense. In this paper, in analogy with complex motions as given by Müller [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. © 2008 Birkhauser.