title: Closest pair of points
body: <p>In
  <a href="http://en.wikipedia.org/wiki/Closest_pair_of_points_problem" rel="noreferrer">http://en.wikipedia.org/wiki/Closest_pair_of_points_problem</a>
  we can see that it mentions that is at most 6 points that is closest to the point on the other half, which can be represented as the graph below:
  <img src="https://i.stack.imgur.com/6CEad.gif" alt="enter image description here"></p>
  
  <p>My question is for point P1 and Point P2, the distance to the red point will exceed sqrt(2)*d, why it is part of the solution? Why it is not at most 4 points that is closest to P rather than at most 6 points? Thanks.</p>