Lines in space

Looks at the following problem: given four lines, K L, M and N, find a fifth line V that intersects all four. This problem was originally solved, and solved well, by Seth Teller and Michael Hohmeyer in their 1999 article that appeared in Journal of Graphics Tools. Teller and Hohmeyer solved the problem purely numerically using singular value decomposition. SVD is one of the more reliable numerical techniques, so their solution is probably the best one to find actual numerical answers. The author's series of articles has been working toward a more symbolic solution, both in the hopes of generating greater geometric intuition on the different typs of solutions possible, and as a springboard for various digressions on the general topic of relating algebra and geometry. In exploring this relations one can either work from geometry to algebra (picking geometric relationships and trying to find algebra to geometry (picking algebraic relationships and trying to find the geometry they represent). The author does the latter.