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Re: Random Triangle Problem
Posted:
Aug 6, 1997 7:07 PM
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In article <5s63dg$pgj$3@cantuc.canterbury.ac.nz>,
mathwft@math.canterbury.ac.nz (Bill Taylor) wrote:
> eclrh@sun.leeds.ac.uk (Robert Hill) writes:
> |> Another question: is there some interesting shape of bounded set
> |> such that the probability is 3/4 for vertices independently and
> |> uniformly distributed within that set?
>
> What an excellent question! I hope someone finds one. Meanwhile we
> need those n-gon results...
I thought it was an excellent question too, and sent an
answer by email. But it turns out to be a triviality.
Consider randomly selecting the vertices from a rectangle of
of height 1. The probability of obtuseness is obvioulsy a
continuous function of the length of the rectangle. As the
square and a long thin rectangle give probabilites either
side of 3/4, the intermediate value theorem says there is
a rectangle with the given property.
--
Terry Moore, Statistics Department, Massey University, New Zealand.
Theorems! I need theorems. Give me the theorems and I shall find the
proofs easily enough. Bernard Riemann
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