Real circles tangent to 3 conics
Fuente:
arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866913821131538432 |
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| author | Breiding, Paul Lindberg, Julia Ong, Wern Juin Gabriel Sommer, Linus |
| author_facet | Breiding, Paul Lindberg, Julia Ong, Wern Juin Gabriel Sommer, Linus |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_06876 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Real circles tangent to 3 conics Breiding, Paul Lindberg, Julia Ong, Wern Juin Gabriel Sommer, Linus Algebraic Geometry 14N10, 14P05, 14N15 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. |
| title | Real circles tangent to 3 conics |
| topic | Algebraic Geometry 14N10, 14P05, 14N15 |
| url | https://arxiv.org/abs/2211.06876 |