Very obvious fact to some, fascinating to me though.
Consider a triangle. Think of it as three points, where three lines intersect. Imagine that we are only dealing with Rational Points (points whose coordinates are rational numbers)
It appears to me, though I have no proof, that each triangle will have the potential to draw upon it an associated set of three circles, all touching each other at one point. (this is also called “mutually tangent” or even “kissing circles”).
I would imagine this is true for any triangle, including funky skinny thin ones
Even in the case where the triangle is just a line, where all points are collinear. There are three circles, it’s just that the middle circle has a radius of zero. Or, you might say, it has infinite curvature. (Curvature being the inverse of Radius, or 1 divided by Radius)
Well…. what happens when you have…
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