[ExI] isaac's number

[Tomaz Kristan]

You can experiment without a random number generator.

8 times nested for loop.

(x1=0;x1+=0.01;x1<1)
(y1=0;y1+=0.01;y1<1)
(x2=0;x2+=0.01;x2<1)
(y2=0;y2+=0.01;y2<1)
(x3=0;x3+=0.01;x3<1)
(y3=0;y3+=0.01;y3<1)
(x4=0;x4+=0.01;x4<1)
(y4=0;y4+=0.01;y4<1)

if (x4,y4) is inside triangle((x1,y1),(x2,y2),(x3,y3)) insider++ else
outsider++


There are some (quite drastic) optimizations possible, but that's
basically that.






On Thu, Aug 3, 2017 at 10:10 AM, BillK <pharos at gmail.com> wrote:

> 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
>
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>



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