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On lines and Joints by Kaplan, Haim; Sharir, Micha; Shustin, Eugenii is a scholarly article available to read on EtoBox.

What is On lines and Joints about?

Let $L$ be a set of $n$ lines in $\reals^d$, 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 simple algebraic proof technique, we show that the maximum possible number of joints of $L$ is $\Theta(n^{d/(d-1)})$. For $d=3$, this is a considerable simplification of the orignal algebraic proof of Guth and Katz~\cite{GK}, and of the follow-up simpler proof of Elekes et al. \cite{EKS}.

Author

Kaplan, Haim; Sharir, Micha; Shustin, Eugenii

Published

2009

Language

EN