Non-Euclidean Visibility Problems

[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.

[学科分类] 数学（综合）

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