On lines and Joints

Haim Kaplan, Micha Sharir, Eugenii Shustin

Let $L$ be a set of $n$ lines in ${\mathbb{R}}^d$, for $d\ge 3$. A {\em joint} of $L$ is a point incident to at least $d$ lines of $L$, not all in a common hyperplane. Using a very simpl…