An Improved Bound for Joints in Arrangements of Lines in Space

Abstract Let L be a set of n lines in space. A joint of L is a point in R3 where at least three non-coplanar lines meet. We show that the number of joints of L is O(n112/69 log6/23n)=O(n1.6232), improving the previous bound O(n1.643) of Sharir.