I am puzzeling with the following:
Using the beltrami klein disk of hyperbolic geometry (see https://en.wikipedia.org/wiki/Beltrami%E2%80%93Klein_model ) (PS not the poincare disk model)
and given a segment inside it
How to construct an equilateral triangle where the segment is one of its sides?
I know you could first translate the endpoints to a Poincare disk points , do the construction the poincare disk and then translate the third point back to the beltrami model.
But is there no simpler way?