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Fun Geometry Problem

  1. Nov 14, 2009 #1
    1. The problem statement, all variables and given/known data
    In R^3, if we have p non-intersecting lines, is it true that there exists a plane Y such that all the lines intersect Y? Up to rotations.


    2. Relevant equations



    3. The attempt at a solution

    No real attempt, this is just something I found to be interesting. Any thoughts?
     
  2. jcsd
  3. Nov 14, 2009 #2
    Here is a better question:

    Is R^3 - {n non-intersecting lines} homeomorphic to R^3 - {n parallel non intersecting lines}?
     
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