File:Hyperbolic ideal triangle and its incircle.svg

Summary

Description	English: An ideal hyperbolic triangle, its incircle and some lengths associated with it, depicted in the Beltrami–Klein model (left) and the Poincaré disk model (right). The radius of the incircle of the ideal triangle is $\| A B \| = \frac{\ln (3)}{2} \approx 0.55$ ^[1] The edge length of the inner contact triangle is $\| A C \| = 2 \ln (φ) \approx 0.96$ where $φ = \frac{1 + \sqrt{5}}{2}$ is the golden ratio^[1] The (orthogonal) distance from one touchpoint to one of the other edges is $\| A D \| = \ln (1 + \sqrt{2}) \approx 0.88$ ^[2]
Date	29 January 2016
Source	Own work
Author	Martin von Gagern

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