Marshall, T. H.; Martin, G. J. Packing strips in the hyperbolic plane. (English) Zbl 1032.52007 Proc. Edinb. Math. Soc., II. Ser. 46, No. 1, 67-73 (2003). Summary: A strip of radius \(r\) in the hyperbolic plane is the set of points within distance \(r\) of a given geodesic. We define the density of a packing of strips of radius \(r\) and prove that this density cannot exceed \[ {\mathcal S}(r)= {3\over\pi} \sinh r \text{arccosh} \left (1+ {1 \over 2\sinh^2r} \right). \] This bound is sharp for every value of \(r\) and provides sharp bounds on collaring theorems for simple geodesics on surfaces. Cited in 2 Documents MSC: 52C15 Packing and covering in \(2\) dimensions (aspects of discrete geometry) 51M09 Elementary problems in hyperbolic and elliptic geometries 51M04 Elementary problems in Euclidean geometries Keywords:Fuchsian group; strip; hyperbolic plane; geodesic; density; packing PDFBibTeX XMLCite \textit{T. H. Marshall} and \textit{G. J. Martin}, Proc. Edinb. Math. Soc., II. Ser. 46, No. 1, 67--73 (2003; Zbl 1032.52007) Full Text: DOI