Quote Originally Posted by OngBonga View Post
So I found out why the probability of looking at a point is 6/pi^2

That just happens to be the probability that you pick two arbitrary whole numbers at random and they are co-prime, that is they have no common denominator. That's the same as looking in a direction on our infinite orchard and seeing a point... that point we see is the first in a line, the first one being the co-prime integers, with all the hidden points behind being the same ratio and therefore not co-prime.

To demonstrate co-prime... 6 and 7 are co-prime, since the only common denominator is 1, however 6 is not prime since it's even. The point (6,7) on our graph is the first point in that line, every hidden point behind it has a common denominator... (12,14) - 2, then (18,21) - 3, then (24, 28) - 4, then (30,35) - 5 etc.

So now we know where the value 6/pi^2 comes from. It's a product of the Riemann Zeta Function.
There's a tree on every pair of whole numbers, so if we're just picking whole numbers at random, then we always look at a tree, right?