The Cauchy-Length Formula and Holditch Theorem in the Generalized Complex Plane C-p

ERİŞİR T., Gungor M. A.

INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY, vol.11, no.2, pp.111-119, 2018 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 2
  • Publication Date: 2018
  • Journal Indexes: Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
  • Page Numbers: pp.111-119
  • Erzincan Binali Yildirim University Affiliated: Yes


In this paper, firstly, we calculate Cauchy-length formula for the one-parameter planar motion in generalized complex plane C-p which is generalization of the complex, dual and hyperbolic planes. Then, we give the length of the enveloping trajectories of lines C-p. In addition, we prove the Holditch theorem for the non-linear three points with the aid of the length of the enveloping trajectories in C-p. So, the Holditch theorem for the linear three points which is given by Erisir et al. in C-p is generalized for trajectories drawn by the non-linear three points in generalized complex plane C-p.