A New Generalization of the Steiner Formula and the Holditch Theorem

ERİŞİR T., GÜNGÖR M. A., TOSUN M.

ADVANCES IN APPLIED CLIFFORD ALGEBRAS, cilt.26, sa.1, ss.97-113, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 26 Sayı: 1
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1007/s00006-015-0559-4
  • Dergi Adı: ADVANCES IN APPLIED CLIFFORD ALGEBRAS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.97-113
  • Erzincan Binali Yıldırım Üniversitesi Adresli: Hayır

Özet

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.