Given two points in the upper half-plane with the usual hyperbolic metric, the geodesic between them is found by drawing a circle through them that crosses the real axis at right angles. However, if I give you coordinates for the points, how do I construct such a circle explicitly? I guess this becomes a question in classical plane geometry, but I don't see how to do it.
How to compute geodesics in upper half-plane?
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geometry
complex-analysis
differential-geometry
1 Answers
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The center of the circle lies on the real axis, and also on the perpendicular bisector of the two points, so...
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0I thought you wanted a Euclidean geometry construction. The same thing works: htt$p$://i.stack.imgur.com/vu9Ry.png – 2012-11-13