Friend of mine saw very interesting triangle centers which are closely located for any triangle. Those are Hofstadter point D (X360: https://en.wikipedia.org/wiki/Hofstadter_points) and the Outer Soddy center E (X176: http://mathworld.wolfram.com/OuterSoddyCenter.html).
The question I have a bit out of scope may be: But can this cause any fundamental physical law or some formula in discrete mathematics? In other words I would like to ask about the applications of this.
EDITED:
And even more if we consider the line connecting Hofstadter 0 and 1 points (X359 and X360) the X176 is located amazingly close to this line. The maximum distance I was able to get is less than 0.05 for triangle with area grater than 15000.
