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In the Poincaré model of hyperbolic geometry, we found a formula relating
the angle measurement of the angle of parallelism and the distance to
which it is associated. This formula is a special case of the general formula
discovered independently by Bolyai and Lobachevsky.
Theorem 17.10: [Formula of Bolyai-Lobachevsky]
where k is the proportionality constant from Theorem 18.9.
We have proven this formula in the Poincaré model where k=1.
droyster@math.uncc.edu