On Problem of Best Circle to Discontinuous Groups in Hyperbolic Plane

Mathematical Communications

article

Arnasli Yahya¹ 

[1] Department of Geometry, Budapest University of Technology and Economics

关键词: Inscribed circle;    Poincare-Delone (Delaunay) Problem;    Discontinuous group;    Hyperbolic plane;   

学科分类：工程和技术（综合）

来源: Sveuciliste Josipa Jurja Strossmayera u Osijeku * Odjel za Matematiku / University of Osijek, Department of Mathematics

【 摘 要 】

The aim of this paper is to describe the largest inscribed circle into the fundamental domains of a discontinuous group in Bolyai-Lobachevsky hyperbolic plane. We give some known basic facts related to the Poincare-Delone problem and the existence notion of the inscribed circle. We study the best circle of the group G = [3, 3, 3, 3] with 4 rotational centers each of order 3. Using the Lagrange multiplier method, we would describe the characteristic of the best-inscribed circle. The method could be applied for the more general case in G = [3, 3, 3, · · ·, 3] with l ≥ 4 rotational centers each of order 3, by more and more computations. We observed by a more geometric Theorem 2 that the maximum radius is attained by equalizing the angles at equivalent centers and the additional vertices with trivial stabilizers, respectively. Theorem 3 will close our arguments where Lemma 3 and 4 play key roles.

【 授权许可】

CC BY-NC-ND