The Joints Problem in $\mathbb{R}^n$
René Quilodrán · SIAM Journal on Discrete Mathematics · 2010
We show that given a collection of A lines in $\mathbb{R}^n$, $n\geq2$, the maximum number of their joints (points incident to at least n lines whose directions form a linearly independent set) is $O(A^{n/(n-1)})$. An analogous result for smooth algebraic curves is also proven.