Research Article

Equality of internal angles and vertex points in conformal hyperbolic triangles

Volume: 41 Number: 3 September 30, 2020
EN

Equality of internal angles and vertex points in conformal hyperbolic triangles

Abstract

In this article, by using the conformal structure in Euclidean space, the conformal structures in hyperbolic space and the equality of the internal angles and vertex points of conformal triangles in hyperbolic space are given. Especially in these special conformal triangles, the conformal hyperbolic equilateral triangle and the conformal hyperbolic isosceles triangle, the internal angles and vertices are shown.

Keywords

References

  1. Asmus, I., Duality Between Hyperbolic and de-Sitter Geometry, Cornell University, New York, (2008) 1-32.
  2. O’neil, B., Semi-Riemannian Geometry, Academic Press., London, (1983) 46-49, 54-57, 108-114, 143-144.
  3. Suarez-Peiro, E., A Schlafli Differential Formula for Implices in Semi-Riemannian Hyperquadrics, Gauss-Bonnet Formulas for Simplices in the de Sitter Sphere and the Dual Volume of a Hyperbolic Simplex, Pasicif Journal of Mathematics, 194(1) (2000) 229.
  4. Karlığa, B., Edge matrix of hyperbolic simplices, Geom. Dedicata, 109 (2004) 1–6.
  5. Karlığa, B., Yakut, A.T., Vertex angles of a simplex in hyperbolic space , Geom. Dedicata, 120 (2006) 49-58.
  6. Alsan, Ö., Conformal Triangles, M.Sc. Thesis, Kastamonu University Institute of Science and Technology, Kastamonu 2015.
  7. Karlığa, B., Savaş, M., “Field Formulas Based on Edge Lengths of Hyperbolic and Spherical Triangles”, Seminar of Mathematics Deparment, Gazi University, Ankara, (2006) 1-6.
  8. Ratcliffe, J.G., “Foundations of Hyperbolic Manifolds”, Springer-Verlag, Berlin, (1994).

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Publication Date

September 30, 2020

Submission Date

April 14, 2020

Acceptance Date

September 1, 2020

Published in Issue

Year 1970 Volume: 41 Number: 3

APA
Tokeşer, Ü., & Alsan, Ö. (2020). Equality of internal angles and vertex points in conformal hyperbolic triangles. Cumhuriyet Science Journal, 41(3), 642-650. https://doi.org/10.17776/csj.719117

As of 2026, Cumhuriyet Science Journal will be published in six issues per year, released in February, April, June, August, October, and December