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Key to getting from 540 triangles to 516 was setting a reasonable threshold (<0.00000001) and then checking the degree to which the points on a candidate triangle came to achieving equality in the triangle inequality. (https://en.wikipedia.org/wiki/Triangle_inequality)
In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side. This statement permits the inclusion of degenerate triangles, but some authors, especially those writing about elementary