Poncelet Triangles and Tetragons over Finite Fields

Milena Radnović; Ruzzel Ragas

doi:10.1016/j.ffa.2026.102815

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arXiv · 2511.06347

Poncelet Triangles and Tetragons over Finite Fields

Milena Radnović·Ruzzel Ragas

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Abstract

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.

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Milena Radnović, Ruzzel Ragas. 2025-11-09. Poncelet Triangles and Tetragons over Finite Fields. https://doi.org/10.1016/j.ffa.2026.102815

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