Partitioning 4 space with ultraskew lines, and the three body problem.

From: Richard L. Peterson (sac23522_at_saclink.csus.edu)
Date: 10/27/04 

Date: Wed, 27 Oct 2004 13:30:08 +0000 (UTC)

Suppose we are in 4 space. Two lines are "skew" if they do not lie in
the same plane(2 space). Skewness is a binary relation on lines. Now
two skew lines will lie in the same 3 space. But it is possible for
three lines to not lie in the same 3 space. This is a ternary relation
on lines. I don't know if there's a name for this relation, so let's
call it "ultraskewness" until we find out.

1) Can one foliate, or at least partition, 4 space with lines that
are tripletwise ultraskew? I mean EACH 3 line subset of the partition
must not lie in the same 3 space.

2) In the three-body problem, one could approximate the trajectory
of each of the 3 masses as a straight lines until they became close
enough to each other for their gravitation to have an appreciable
effect. I think much of the work on this problem assumes all three
trajectories lie in the same plane.(The restricted 3-body problem.)
But some work has been where the trajectories are not coplanar.
Wouldn't it be fun to explore the three-body problem when the
trajectories are not cospatial?

Richard Peterson, CSU Sacramento

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