[ExI] isaac's number

spike spike66 at att.net
Thu Aug 3 05:52:41 UTC 2017



From: extropy-chat [mailto:extropy-chat-bounces at lists.extropy.org] On Behalf Of spike
Subject: Re: [ExI] isaac's number




From: extropy-chat [mailto:extropy-chat-bounces at lists.extropy.org] On Behalf Of John Clark
Sent: Wednesday, August 02, 2017 6:00 AM
To: ExI chat list <extropy-chat at lists.extropy.org <mailto:extropy-chat at lists.extropy.org> >
Subject: Re: [ExI] isaac's number


On Tue, Aug 1, 2017 at 2:10 PM, spike <spike66 at att.net <mailto:spike66 at att.net> > wrote:


>>>...Woolhouse's 11/144 = .076388889, equal to my Monte Carlo solution to about a part per million.

​ ​

>>>…Correction, my sim gives .0763889013, but I found a much faster way to do the calc by generating only three points and calculating an area.



>>…That my friend is impressive!  John Clark 



>…John as much as I would like to soak up that sentiment, I can’t claim credit.  The really impressive feat was the closed form solution found by Woolhouse.  spike




OK, news from the geek-with-too-much-time-on-his-hands department: I took my Monte Carlo sim for the triangles and generalized it to 3 dimensions.


Original question:  in a unit square with three random points, what is the average area of the triangle?


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.


Guesses?  Higher or lower than 0.00849?







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