Abstract
Any two non-intersecting circles have a kind of distance that is invariant for inversion, namely, the natural logarithm of the ratio of the radii (the larger to the smaller) of two concentric circles into which the given circles can be inverted. When the inversive plane is used as a conformal model for hyperbolic space [3, p 266], the inversive distance between two non-intersecting circles is equal to the hyperbolic distance between the corresponding ultra-parallel planes.
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