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


ERİŞİR T. , Gungor M. A.

INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY, cilt.11, no.2, ss.111-119, 2018 (ESCI İndekslerine Giren Dergi) identifier

  • Cilt numarası: 11 Konu: 2
  • Basım Tarihi: 2018
  • Dergi Adı: INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY
  • Sayfa Sayıları: ss.111-119

Özet

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.