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 \({p \in \mathbb{R}}\) we generalized the Steiner Formula and Holditch theorem consisting the Euclidean \({\left({p = -1}\right)}\), Galilean \({\left({p = 0}\right)}\) and Lorentzian \({\left({p = 1}\right)}\) cases.
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Erişir, T., Güngör, M.A. & Tosun, M. A New Generalization of the Steiner Formula and the Holditch Theorem. Adv. Appl. Clifford Algebras 26, 97–113 (2016). https://doi.org/10.1007/s00006-015-0559-4
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DOI: https://doi.org/10.1007/s00006-015-0559-4