Illustration of equilateral hyperbolic triangles

The CabriJava window shows an equilateral hyperbolic triangle ABC. If you drag B along the cyan h-line, the h-triangle remains equilateral. You should observe that as B approaches the boundary, the angles become small. It is not really obvious that they are equal! The cyan circles were used in the construction. Ka is the h-circle with h-centre A, through B, and Kb is the h-circle with h-centre B, through A. These meet in C, so that d(A,B) = d(B,C) = d(C,A). The h-circles meet again at C', giving another equilateral h-triangle, h-congruent to ABC. This shows how different such h-triangles can look in our model.


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