# Triangle-Closed Planar Sets

Triangle-Closed Planar Sets

You are given a special triangle (or a set of three non-collinear points) as a seed for a subset of the plane.

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For all pairs of points A, B in you are asked to find the "closure point" C = C() such that the triangle ABC is similar to .

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Once C is found, we add it to the set .

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The cases where is not a dense subset of the plane are the most interesting ones. Can you find a few?

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Several examples of non-dense sets are given (choose one from the "closed set" options).

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