{"paper":{"title":"On the Poncelet triangle condition over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jaydeep Chipalkatti","submitted_at":"2016-04-01T23:38:40Z","abstract_excerpt":"Let ${\\mathbf P}^2$ denote the projective plane over a finite field ${\\mathbb F}_q$. A pair of nonsingular conics $({\\mathcal A}, {\\mathcal B})$ in the plane is said to satisfy the Poncelet triangle condition if, considered as conics in ${\\mathbf P}^2({\\overline{\\mathbb F}}_q)$, they intersect transverally and there exists a triangle inscribed in ${\\mathcal A}$ and circumscribed around ${\\mathcal B}$. It is shown in this article that a randomly chosen pair of conics satisfies the triangle condition with asymptotic probability $1/q$. We also make a conjecture based upon computer experimentation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00436","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}