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

05/28/2020

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by   Andrey Sergunin, et al.

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We consider the following question: Given n lines and n circles in 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).