By the Poincaré disk model Escher believed the lines bisecting the fish meet the boundary of the disk at 90 degrees but it was actually proven to be about 80 degrees and the lines are called hypercycles.
Bending the Rules of Geometry
Hyperbolic geometry may be partially responsible for breakthroughs in physics such as general relativity and quantum field theory. But we're not used to seeing curved environments like the ones in this video. Enter a world that defies our basic assumptions about the rules of geometry.