Tetrahedral Treats

Have you ever wondered about the geometry of tetrahedra? It would seem that there should be some fascinating results, like those for a triangle, but you never see any reference to them.

Computer algebra systems and 3D construction software make the study of solid geometry accessible to more students. A TI-89 graphing calculator [or Mathematica, which I use in this article since the visual display of Mathematica is cleaner than that of the TI-89] allows quick computations that would be tedious and time-consuming if done by hand. This Geometer's Corner is about how you can use Cabri 3D, a 3D construction program, and a computer algebra system such as that on a TI-89 to study tetrahedra. As I metnioned earlier it should come as no surprise that many of the special properties of triangles have 3D equivalents. In what follows we will look for the 3D equivalents of the four special points that every triangle has.