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On the Poncelet triangle condition over finite fields
Let denote the projective plane over a finite field . A pair of nonsingular conics in the plane
is said to satisfy the Poncelet triangle condition if, considered as conics in
, they intersect transverally and
there exists a triangle inscribed in and circumscribed around
. It is shown in this article that a randomly chosen pair of
conics satisfies the triangle condition with asymptotic probability . We
also make a conjecture based upon computer experimentation which predicts this
probability for tetragons, pentagons and so on up to enneagons