Solution of Scott's problem on the number of directions determined by a point set in 3-space

Let P be a set of n points in Ê3 , not all in a common plane. We solve a problem of Scott (1970) by showing that the connecting lines of P assume at least 2n − 7 different directions if n is even and at least 2n − 5 if n is odd. The bound for odd n is sharp.

• Type: Conference
• Year: 2004
• Where: COMPGEOM
• Authors: János Pach, Rom Pinchasi, Micha Sharir
• Keywords: Common Plane, COMPGEOM 2004