Interesting I should say... Anyway a couple of points on the discussion we had so far...
1. We cannot bound the triangle if we don't bound the space...thats the reason why I choose a unit square 2. It is true that there are a lot of points outside the triangle that you cannot choose but they all lie in a finite set of lines Cheers, Nat On 3/8/07, Karthik Singaram L <[EMAIL PROTECTED]> wrote: > > The question as it seems is known as the "Sylvesters Question" > I quote from the paper "Random points, convex bodies, lattices" by Imre > barany. > > "Show the chance of four points forming the apices of a reentrant > quadrilateral is 1/4 if they are taken at random in an indefinite plane". It > was understood within a year that the question is ill-posed.(The culprit is, > as we all know by now, the "indefinite plane" since there is no natural > probability measure on it.) So Sylvester modi ed the question: let K be a > convex body and choose four random, independent points uniformly from K, > and write P (K) for the probability that the four points form the apices of > a reentrant quadrilateral, or, in more modern terminology, that their convex > hull is a triangle. How large is P (K)?, and for what K is P (K) the largest > and the smallest? This question became known as Sylvester's four-point > problem. It took fifty years to find the > answer................................ > > You can google for cool solutions to generalized versions of the > Sylvester's problem....for many versions just bounds exist but no exact > solutions. > > > > --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to algogeeks@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/algogeeks -~----------~----~----~----~------~----~------~--~---
