Posts Tagged ‘circles’

Ok, this post has no use whatsoever, but I need to get this out of my system. I was in an incredibly dull meeting the other day, and at one point, I had on my sheet of notes 3 randomly placed dots:

 
.
 
             .
   .
 

For some reason, I don't know why, I started to wonder if there would be one or more circles that have an outline that touches these 3 dots. Yes I am a nerd (just imagine how boring the meeting was).

To put this puzzle in other words: is there, for any given set of 3 points, a 4th point that has an equal distance to the first 3 points?

My preliminary conclusion is that for each three points, there is exactly 1 circle that has a matching outline, unless the 3 points are positioned exactly in one line. I lack the mathematical background however to prove/disprove this in theory. I discussed this with a fellow nerd and he also concluded that there should be exactly 1 circle for each set of 3 points (as long as they are not in a straight line).

Now I'm curious. Am I right in the 'exactly 1 circle' assumption? If so, what would be the optimal way of determining the center of the circle? In other words, how would you implement:

 
/**
 * Determine the center point of a circle whose outline strikes 3 given points.
 * @param Point $a
 * @param Point $b
 * @param Point $c
 * @return Point The center point of the circle outlining point $a, $b and $c
 */
function centerpoint($a, $b, $c)
{
  ....
  return new Point($x, $y);
}
 

On to something else. The rumours of the Zend Framework are spreading quickly. I haven't been contacted by Zend so it's not going to be Zend ATK. I'm wondering what it is though. Whether it's anything like a business framework, or more of an IDE kind of thing, or just a set of classes providing some API.

Finally an update on ATK: we're wrapping up RC1 of ATK 5.3. It should be out real soon now.