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.

return to congruence page