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Non-Euclidean visibility problems

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Abstract

We consider the analog of visibility problems in hyperbolic plane (represented by Poincaré half-plane model ℍ), replacing the standard lattice ℤ × ℤ by the orbitz = i under the full modular group SL2(ℤ). We prove a visibility criterion and study orchard problem and the cardinality of visible points in large circles.

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  1. Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049, Madrid, Spain

    Fernando Chamizo

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  1. Fernando Chamizo
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Chamizo, F. Non-Euclidean visibility problems. Proc. Indian Acad. Sci. (Math. Sci.) 116, 147–160 (2006). https://doi.org/10.1007/BF02829784

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