Hyperbolic Soccerballs

Frank Sottile

   We are all familiar with basic Euclidean geometry 
of the plane, including the behaviour of parallel lines
and angles in triangles.  In fact, we are so familiar
with this, that we think it is a law of nature.

   In this activity (it is not a lecture), we will 
all build two-dimensional models of negatively curved
(hyperbolic) space and then explore the basic geometry
of parallel lines and triangles in the hyperbolic plane.