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Topic: Lines in the plane
Replies: 7   Last Post: Apr 27, 2001 5:21 PM

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Posts: 31
Registered: 12/13/04
Re: Lines in the plane
Posted: Apr 26, 2001 7:28 PM
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"Mike Schubert" <> wrote in message
> How it can be proved that for n>=3, n distinct points in the plane,
> not all on a single line, determine at least n distinct lines ?

Suppose that exactly k of the points lie on the same line
for some k ( 2 <= k < n ). Then each of the remaining
n - k points can be paired with each of these points leading
to (n - k)*k distinct lines. Along with the first line this leads
to 1 + (n-k)*k lines which is >= n for n >= 3.


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