points and triangles in the plane and halving planes in space
We prove that for any set S of n points in the plane and n 3-&agr; triangles spanned by the points of S there exists a point (not necessarily of S ) contained in at least n 3-3&agr; /(512 log 5 n ) of the triangles. This implies that any set of n points in three-dimensional space defines at most 6.4 n 8/3 log 5/3 n halving planes.
point space