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




Re: Lines in the plane
Posted:
Apr 26, 2001 7:28 PM


"Mike Schubert" <mikeschub2@iol.com> wrote in message news://yifcfwkp2kcn@forum.mathforum.com... > 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 + (nk)*k lines which is >= n for n >= 3.
Regards, S.K.Mody.



