A New Generalization of the Steiner Formula and the Holditch Theorem


ERİŞİR T., GÜNGÖR M. A. , TOSUN M.

ADVANCES IN APPLIED CLIFFORD ALGEBRAS, vol.26, no.1, pp.97-113, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 26 Issue: 1
  • Publication Date: 2016
  • Doi Number: 10.1007/s00006-015-0559-4
  • Journal Name: ADVANCES IN APPLIED CLIFFORD ALGEBRAS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.97-113
  • Erzincan Binali Yildirim University Affiliated: No

Abstract

In this study, we first obtained the Steiner area formula in the generalized complex plane. Then, with the aid of this formula, we determined a new approach for the Holditch theorem giving the relationship between the areas formed by points in the generalized complex plane (or p-complex plane). Finally, according to the special values of p = -1, 0, 1 we examined the cases of the Steiner Formula and Holditch Theorem. In this way, for we generalized the Steiner Formula and Holditch theorem consisting the Euclidean , Galilean and Lorentzian cases.