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arXiv · 2005.14043

On the number of intersection points of lines and circles in $\mathbb R^3$

Andrey Sergunin
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Abstract

We consider the following question: Given $n$ lines and $n$ circles in $\mathbb{R}^3$, what is the maximum number of intersection points lying on at least one line and on at least one circle of these families. We prove that if there are no $n^{1/2}$ curves (lines or circles) lying on an algebraic surface of degree at most two, then the number of these intersection points is $O(n^{3/2})$.

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Andrey Sergunin. 2020-05-28. On the number of intersection points of lines and circles in $\mathbb R^3$. https://arxiv.org/abs/2005.14043

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