[ExI] isaac's number
pharos at gmail.com
Thu Aug 3 08:10:29 UTC 2017
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.....
More information about the extropy-chat