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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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June 24, 2012 at 5:35 pmPoincare Disk Model of Hyperbolic Geometry « Unknown Blogger …  mathematica