Holditch theorem and Steiner formula for the planar hyperbolic motions

YÜCE S., KURUOĞLU N.

Advances in Applied Clifford Algebras, vol.20, no.1, pp.195-200, 2010 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 1
  • Publication Date: 2010
  • Doi Number: 10.1007/s00006-008-0130-7
  • Journal Name: Advances in Applied Clifford Algebras
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.195-200
  • 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, 5] were expressed by Müller, under the one-parameter closed planar motions in the complex sense. Also, Müller had iven Holditch theorem1 in the complex sense, [6]. In this paper, in analogy with Complex motions as given by Müller [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. © 2008 Birkhäuser Verlag Basel/Switzerland.