Given $n$ points in $2$-dimensional plane, find a pair of points with the following properties:
Suppose the two points are $(x_1,y_1)$ and $(x_2,y_2)$. We find their midpoint(s), say, $(x_3,y_3)$, and draw a line of slope $\pm 1$ on the point $(x_3,y_3)$. Let's call this line $L$.
By geometry, the distance of points $(x_1,y_1)$ and $(x_2,y_2)'$ from the line $L$ is the same. Let that distance be $x$.
We want to find pair of points with minimum distance of $x$.
It is a programming problem , but I want to know if it can be used solving mathematics. :-)
Example : - Say,the following 3 points :-
The required pair is :- $([0,1],[1,0])$, for which $x= 0$