Illinois Geometry Lab

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IGL Projects, 2011

Linear Algebra Demonstrations

Rob Halliday, Andrew Lee

VectorSpan2D: A Mathematica notebook demonstrating the span of two vectors in two-dimensional space. Use CDF player or Mathematica to view the app below, or download the .nb file for the source code.

Click below to activate the demonstration.

Basic Physics of Hyperbolic 3-Space

Anton Lukyanenko and Platon Lukyanenko
Mathematica and POV-Ray
Download Project Files

In hyperbolic space, things look smaller as they get closer to the XY plane, so a ball traveling straight will look like it's changing size and moving along a curved line. Collisions are defined infinitesimally by Euclidean physics, but these have to be adjusted for non-infinitesimal objects. In the simulation, the balls can't bounce out of the green sphere. The video below shows the same balls from a different view, where hyperbolic space fits entirely within a single sphere.