Non-Euclidean Visibility Problems

Proceedings Mathematical Sciences

Fernando Chamizo¹ 

[1] Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 0 Madrid, Spain$$

关键词: Modular group;    hyperbolic plane;    Poincaré half-plane model.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

We consider the analog of visibility problems in hyperbolic plane (represented by Poincaré half-plane model $mathbb{H}$), replacing the standard lattice $mathbb{Z} × mathbb{Z}$ by the orbit 𝑧 = 𝑖 under the full modular group $SL_2(mathbb{Z})$. We prove a visibility criterion and study orchard problem and the cardinality of visible points in large circles.

【 授权许可】

Unknown