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Topic: Question from the classroom: Geometry
Replies: 2   Last Post: Jun 16, 1996 9:45 PM

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Jerry Grossman

Posts: 25
Registered: 12/6/04
Re: Question from the classroom: Geometry
Posted: Jun 15, 1996 11:26 AM
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Ray Steiner wants to know if all numbers of intersection points are possible
between n-1 and n(n-1)/2 if n>3 lines are arranged (in a plane or more
generally?).

I don't know the answer, but thirty-odd years ago I worked on the dual
question: for which k is it possible to arrange n points in the plane so
that the number of lines they determine is k? A classic result is that k
cannot be strictly between 1 and n, and obviously k cannot exceed
n(n-1)/2. A few other values are seen to be excluded, as well (e.g., I
believe that a friend of mine showed that you can't get 8 lines from 7
points, as part of his project that took him to the finals of the
Westinghouse Science Talent Search). So people looking at Steiner's
question can look at this one as well.
Jerry Grossman
Oakland University







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