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I have two fixed points, $P_1$ and $P_2$. I am trying to distribute $n$ points between them, so that the distance between every point is equal. This is easy when:

distance between points $\cdot (n-1) =$ distance between $P_1$ and $P_2$,

as they all follow the slope of the two fixed points, but I want to be able to increase the distance between them so that:

distance between points $\cdot (n-1) >$ distance between $P_1$ and $P_2$.

I have played around a lot with pythagorean methods, but I always seem to be one variable short.

Thanks for any help.

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    Do you want those $n$ points to like on the line between $P_1$ and $P_2$? In that case there is just one way to do it, and the distance between new points will be $|P_1-P_2|/(n+1)$. (Or $|P_1-P_2|/(n-1)$ depending on how you count points.) If you allow the points to be elsewhere on the plane, you can arrange them along a circular arc to create more space between.2012-06-25
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    Hi yes I want to arrange the points elsewhere on the plane, so the total distance between all points is greater than the distance between p1 and p2.2012-06-25
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    What do you mean with 'total distance between all'? It should be $\sum d(q_i,q_j)$?2012-06-25

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