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Topic: Simplex construction
Replies: 1   Last Post: Nov 21, 2013 3:28 PM

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Avni Pllana

Posts: 546
Registered: 12/6/04
Re: Simplex construction
Posted: Nov 21, 2013 3:28 PM
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> If you break a stick into six randomly sized pieces,
> what is the probability that they will form a
> tetrahedron?
> Can you do it for (n*n-n)/2 pieces to form an n
> simplex? So far, the only thing that I have to go on
> is
> That the largest piece can't be longer than the total
> length of the other pieces as would be true if we
> were building a triangle (2 simplex). Thanks in
> advance for any help.

Hi Patrick,

by numeric experiments I obtained following values:

p(2) = 0.25 = 1/4 ,
p(3) = 0.0666 ~ 1/4^2 ,
p(4) = 0.01773 ~ 1/4^3 ,
p(5) = 0.004776 ~ 1/4^4 .

Hope this helps,

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