A Counter-Example to the Theorem of Hiemer and Snurnikov

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A planar polygonal billiard 𝓅 is said to have the finite blocking property if for every pair (O, A) of points in 𝓅 there exists a finite number of “blocking” points B1,…, Bn such that every billiard trajectory from O to A meets one of the Bi's. As a counter-example to a theorem of Hiemer and Snurnikov, we construct a family of rational billiards that lack the finite blocking property.

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