Work

Poncelet triangles and tetragons over finite fields

Year: 2026

Type: article

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.

Source: Finite Fields and Their Applications

DOI: 10.1016/j.ffa.2026.102815

Authors: Milena Radnović, Ruzzel Ragas

Language: English

Topic: Mathematics and Applications

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,720

Funders: University of Sydney, Science Fund of the Republic of Serbia, Australian Research Council

Award: G6541809449