[ExI] isaac's number

[BillK]

On 1 August 2017 at 07:28, spike  wrote:
>
> Generate three random points on a square plane to create a triangle.  What
> is the probability that a fourth randomly-generated point will be inside the
> triangle?
>
> He and I wrote sims and both get the same answer to four significant digits:
> 0.0764 but neither of us know how to find it in closed form.  My intuition
> suggested that number should have been 0.125 but it differs from our
> sim-generated Isaac’s number by about phi.  Why phi?  That hasta be a
> coincidence, ja?  Come on math geeks, let us reason together, shall we?
>


I think this gives the solution.
It just needs to be translated into English!   :)

<http://mathworld.wolfram.com/SquareTrianglePicking.html>


BillK