There are n points in a w dimensional Euclidean space such that no w+1 points lie in a co(w-1) dimensional space. (eg. For a plane no 3 points are collinear or for 3D space no 4 are coplanar.) Is it possible to formulate a general formula giving the maximum percentage of acute angled triangles between such points in terms of n & w? (n>2,w>1)
I was motivated to formulate this question by generalizing another question I encountered yesterday, which had been asked in a slightly different version in IMO 1970 relating to the same case for n= 100 & w= 2. It appears it could lead to an interesting answer.