A Poncelet Criterion for Special Pairs of Conics in $PG(2,p^m)$

DOI10.36890/iejg.590595zbMath1456.51005arXiv1409.3035OpenAlexW3008376694MaRDI QIDQ5147060

Katharina Kusejko, Norbert Hungerbühler

Publication date: 2 February 2021

Published in: International Electronic Journal of Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.3035

zbMATH Keywords

quadratic residuespencil of conicsfinite projective planesPoncelet's theorem

Mathematics Subject Classification ID

Finite affine and projective planes (geometric aspects) (51E15) Combinatorial aspects of finite geometries (05B25) Elementary problems in Euclidean geometries (51M04) Combinatorial structures in finite projective spaces (51E20) Non-Desarguesian affine and projective planes (51A35)

Related Items (2)

Complex caustics of the elliptic billiard ⋮ On the Poncelet triangle condition over finite fields

Cites Work

• Simultaneous diagonalization of conics in \(\mathrm{PG}(2,q)\). A finite-geometry approach for simultaneous diagonalization of symmetric \(3\times 3\) matrices in \(\mathrm{GF}(q)\)
• Poncelet's closure theorem
• On Cayley's explicit solution to Poncelet's porism
• Poncelet Porisms and Beyond
• On the mutual position of two irreducible conics in PG(2, q), q odd
• A Simple Proof of Poncelet's Theorem (on the Occasion of Its Bicentennial)
• Geometry. I, II. Transl. from the French by M. Cole and S. Levy
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