Background: This is for an app I'm trying to build around finding the center point between 3 or more people. Between 2 people is pretty simple but was unsure for more than 3.
Edit: from reading the comments, if there is no center - I guess asking for the center point is completely the wrong question. What about then the point where the overall distance traveled by the 3 people as a sum is the minimum?
$\endgroup$ 61 Answer
$\begingroup$As commenters have mentioned, there is no well-defined centre. One useful, easy to calculate 'centre' is the centroid: where the balancing point would be if all the people weighed the same amount and were standing on a weightless plane. If the coordinates of the people are $(x_1, y_1), (x_2, y_n), \cdots , (x_n, y_n)$ then the centroid is at $(\bar x, \bar y) = (\dfrac{x_1+x_2+\cdots+x_n}{n}, \dfrac{y_1+y_2+\cdots+y_n}{n})$.
It also has the advantage that the calculation works for $n=1$ and $n=2$ people.
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