Home > Mathematica > Poincare Disk Model of Hyperbolic Geometry

Poincare Disk Model of Hyperbolic Geometry

The Maurits Cornellis Escher image above (Circle Limit IV, also known  as “Angels and Demons” or “Angels and Devils”) illustrates the Poincare disk representation for hyperbolic geometry. This was the inspiration for the International Mathematica Symposium logo.

In Triangles on Poincare Disk, I use Mathematica to look at the shape of triangles on this Poincare disk.

This CDF is imperfect (a work in progress).  It uses the following:

  • there is a unique line connecting two points on the disk
  • lines in this representation are circles orthogonal to the bounding circle
  • the method used for determining the unique line finds the circumcenter of the two given points and a constructed point from one of the points. A circle through the given and constructed point and orthogonal to the bounding circle is given.
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Categories: Mathematica

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