A New Generalization of the Steiner Formula and the Holditch Theorem

作者:Erisir Tulay; Gungor Mehmet Ali; Tosun Murat*
来源:Advances in Applied Clifford Algebras, 2016, 26(1): 97-113.
DOI:10.1007/s00006-015-0559-4

摘要

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.