If n points lie in a plane and no three are collinear, prove that there are 1/2n(n-1) lines joining these points. I'm not really sure where to even start with proving this. I'm supposed to use proof by induction. Any help would be great. Thanks.

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- October 11th 2013, 08:08 PMclintonh0610Proof by Induction
If n points lie in a plane and no three are collinear, prove that there are 1/2n(n-1) lines joining these points. I'm not really sure where to even start with proving this. I'm supposed to use proof by induction. Any help would be great. Thanks.

- October 11th 2013, 08:42 PMibduttRe: Proof by Induction
something appears to be wrong in the question because 1/2n(n+1) is a fraction and number of lines cannot be in fraction.

- October 12th 2013, 03:56 AMPlatoRe: Proof by Induction
There is nothing wrong with the formula. It just written poorly.

It is . To prove that by induction is a pain.

The base case is trivial: there is no line segment.

Suppose it is true for , there are points and line segments.

If you add one more point, then how many new line segments are added?

See if you can get