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arXiv · 2211.06876

Real circles tangent to 3 conics

Paul Breiding·Julia Lindberg·Wern Juin Gabriel Ong·Linus Sommer
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Abstract

In this paper we study circles tangent to conics. We show there are generically $184$ complex circles tangent to three conics in the plane and we characterize the real discriminant of the corresponding polynomial system. We give an explicit example of $3$ conics with $136$ real circles tangent to them. We conjecture that 136 is the maximal number of real circles. Furthermore, we implement a hill-climbing algorithm to find instances of conics with many real circles, and we introduce a machine learning model that, given three real conics, predicts the number of circles tangent to these three conics.

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Paul Breiding, Julia Lindberg, Wern Juin Gabriel Ong, Linus Sommer. 2022-11-13. Real circles tangent to 3 conics. https://doi.org/10.4418/2023.78.1.5

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