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Advances in Applied Clifford Algebras

, Volume 19, Issue 1, pp 155–160 | Cite as

Holditch Theorem and Steiner Formula for the Planar Hyperbolic Motions

  • Salim Yüce
  • Nuri Kuruoğlu
Article
  • 60 Downloads

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.

Keywords.

Holditch Theorem hyperbolic motion hyperbolic numbers 

Mathematics Subject Classification (2000).

53A17 11E88 

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Copyright information

© Birkhauser 2008

Authors and Affiliations

  1. 1.Faculty of Arts and Science, Department of MathematicsYıldız Technical UniversityİstanbulTurkey
  2. 2.Faculty of Arts and Science, Department of Mathematics and Computer SciencesUniversity of BahçeşehirİstanbulTurkey

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