Poncelet triangles and tetragons over finite fields
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.
Fields of Study & Subjects
Mathematics and Applications
Mathematical Dynamics and Fractals
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Finite Fields and Their Applications
- Publisher
- Elsevier BV
- Volume
- 112
- Pages
- 102815–102815
- Publication date
- 26 February 2026
- Language
- EN