Please reference this
problem.
In the above referenced problem a debate was raised as to the validity of
given solution. This debate caused me to ponder the following problem.
If you place 3 points in a line then obviously every line through any 2
points will intersect exactly 3 points. Now the real question is, is it possible to place more than 3 points in a plane such that all lines between any 2 points intersect exactly 3 points, no more no less.
If the answer to the above question is in the negative, prove it. Otherwise, derive the appropriate example(s),
(In reply to
re: Proof by Michael Kornrade)
"H is an artificial point, where the perpendicular from A intersects BC. It may not be part of the N points."
I think the proof would be more complete by allowing H to coincide with one of the points. Then a case would be included where D coincides with H, and the same logic applies as for D between H and C or between H and B.
Without inclusion of this case, one could say "What if the shortest nonzero distance occurred where the perpendicular from the outside point coincided with one of the N points?"

Posted by Charlie
on 20081214 13:03:37 