Poncelet Triangles and Tetragons over Finite Fields
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912966788513792 |
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| author | Radnović, Milena Ragas, Ruzzel |
| author_facet | Radnović, Milena Ragas, Ruzzel |
| contents | In the projective plane over a finite field of characteristic not equal to 2, we compute the probability that a randomly selected pair of distinct conics $(\mathscr{A},\mathscr{B})$, with $\mathscr{A}$ smooth or singular and $\mathscr{B}$ smooth, in a fixed pencil of conics will admit a triangle or a tetragon inscribed in $\mathscr{A}$ and circumscribed about $\mathscr{B}$. We do this for all pencils, classified up to projective automorphism, with at least one smooth conic; effectively allowing the case where our conic pairs intersect non-transversally. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_06347 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Poncelet Triangles and Tetragons over Finite Fields Radnović, Milena Ragas, Ruzzel Algebraic Geometry 60C05, 51N15, 51E15, 11T06, 11G20, 51N35 In the projective plane over a finite field of characteristic not equal to 2, we compute the probability that a randomly selected pair of distinct conics $(\mathscr{A},\mathscr{B})$, with $\mathscr{A}$ smooth or singular and $\mathscr{B}$ smooth, in a fixed pencil of conics will admit a triangle or a tetragon inscribed in $\mathscr{A}$ and circumscribed about $\mathscr{B}$. We do this for all pencils, classified up to projective automorphism, with at least one smooth conic; effectively allowing the case where our conic pairs intersect non-transversally. |
| title | Poncelet Triangles and Tetragons over Finite Fields |
| topic | Algebraic Geometry 60C05, 51N15, 51E15, 11T06, 11G20, 51N35 |
| url | https://arxiv.org/abs/2511.06347 |