email@example.com (KRamsay) wrote: >In article <firstname.lastname@example.org>, tony richards ><email@example.com> writes: > >|My final question is , 'why persist in believing that the probabilities >for each >|vertex being obtuse must be the same', when it is clear that, given the >first >|two points, > >What do you mean by "first two"? One is picking a triangle at random. > I mean that before you can 'pick a triangle' you first have to construct it and the original post referred to the method of construction involving 'choosing' three points 'at random' on a (presumably flat) surface, the points being made the verteces of a triangle. So I was referring to the first two of the triple of points making up the verteces of a triangle.
My argument is and remains, generating triangles by joining up three randomly generated points (over an infinite plane) will produce a slightly different proportion of obtuse angles triangles (0.7648414 , which = 1 -(1/3)+pi/32) than the proprtion (0.75) which will be produced by generating triangles as the included space between three randomly generated straight lines (random in direction and location on the plane).
-- Tony Richards 'I think, therefore I am confused' Rutherford Appleton Lab ' UK '