
Re: Random Triangle Problem
Posted:
Aug 4, 1997 10:33 PM


eclrh@sun.leeds.ac.uk (Robert Hill) writes:
> To say the same thing > slightly differently, it was not for me obvious a priori that it was right > to assume the vertices to be independently and uniformly distributed on the > circumcircle. Why should there not be a tendency for them to be a bit > bunched, or a bit dispersed?
Indeed, good point. A priori it is not at all obvious they should be independent. But closer inspection reveals that it is merely a somewhat disguised form of the anglesatthecentreandatthecircumference result.
> 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 ngon results...
 Bill Taylor W.Taylor@math.canterbury.ac.nz  There was never a problem so difficult, but that if you just looked at it in the right way  it became even more difficult! 

