:I think the Equidistant curve article answers your question at least in the two-dimensional case, assuming that by \ mathbb { D } you mean the Poincar?disk model . talk ) 01 : 00, 8 March 2011 ( UTC)
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Escher carefully studied Coxeter's figure, marking it up to analyse the successively smaller circles { { efn | Schattschneider notes that Coxeter observed in March 1964 that the white arcs in " Circle Limit III " " were not, as he and others had assumed, badly rendered hyperbolic lines but rather were branches of equidistant curves ."
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