Poincaré Hyperbolic Tiling

Poincaré Hyperbolic Tiling : The area inside this circle represents a hyperbolic plane filled with “ideal triangles”. Notice that all the angles inside these triangles go to zero at the edge of the circle. This image was generated using a series of reflections called anti-homographies. I recently learned about homographies while participating at the Experimental Geometry Lab at the University of Maryland. The right animation shows how a single homography can transform the upper half plane into the Poincaré disk. See also my POV-Ray code, Mathematica code, homography test, and circle inversion.

Hyperbolic Links


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