The Maximum Number of Empty Congruent Triangles Determined by a Point Set
نویسندگان
چکیده
Let be a set of points in the plane and consider a family of (nondegenerate) pairwise congruent triangles whose vertices belong to . While the number of such triangles can grow superlinearly in — as it happens in lattice sections of the integer grid — it has been conjectured by Brass that the number of pairwise congruent empty triangles is only at most linear. We disprove this conjecture by constructing point sets with empty congruent triangles. AMS 2000 Subject Classification: 52C10, 05B07.
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