[ExI] isaac's number

[BillK]

On 3 August 2017 at 06:52, spike wrote:
>
> New question: in a unit cube with four random points, what is the volume of
> the tetrahedron?
>
> I studied that Woolhouse page BillK found, struggled with the integrals for
> a while and finally had to admit that I suck.  I won’t be channeling The
> Donald any time soon.  But I can write Monte Carlo sims of anything that
> moves and plenty of things that do not, so I did.  I just finished it and
> haven’t even run it yet.  Before I pull the trigger, I want to allow us to
> make guesses on what the answer will be.
>
> Last time, my mathematical intuition fell flat, but I want to try again.
> For reasons I will not explain, I now think this answer will come out
> somewhere around 0.00849.
>
> If you want to enter a guess, do so, or if you want to be less committed,
> just say higher or lower than my 0.00849.  The grand prize will be my
> undying respect for all eternity, or until I forget, whichever comes first.
>
> If anyone here generalizes the Woolhouse integrals, I will totally bow down
> before you and declare my grubby self unworthy to gaze upon your brilliance.
> I will be seriously impressed as all hell and say good things about you.
>
> Alternative: BillK might find us another miracle page somewhere that answers
> the new question.
>

Wolfram does say - 'The integral is extremely difficult to compute.'
(If it is difficult for Wolfram...........)  :)

Wolfram gives the answer as 0.01384277.....

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


BillK