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

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Randy Poe

Posts: 1,185
Registered: 12/6/04
Re: Lines in the plane
Posted: Apr 26, 2001 12:04 PM
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On 26 Apr 2001 08:54:44 -0400, mikeschub2@iol.com (Mike Schubert)
wrote:

>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 ?


Sounds like a natural for induction, with a little twist. Work it out
for n=3. Then try n=4.

The twist is that for general n, it seems to me you have to take two
different cases: (1) n-1 points are colinear, and you are adding one
more, or (2) there are no sets of n-1 points which are colinear, in
which case the induction hypothesis holds.

- Randy







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