heilbronn-convex-3-8
For n = 3 through n = 8, this formalization determines the supremal minimum triangle area among n indexed planar points whose own convex hull has Lebesgue area one. It proves a pointwise upper bound, attainment, and the exact value for every n in that range. The values are 1, 1/2, (5-sqrt(5))/10, 1/6, 1/9, and, at n = 8, the unique root in (79/1000, 81/1000) of 2060x^5 - 2332x^4 + 1064x^3 - 240x^2 + 26x - 1. For n = 3, 4, 5, 6, and 8 it also proves pairwise uniqueness of optimizers modulo arbitrary relabeling and arbitrary nonsingular affine transformations. Uniqueness is false at n = 7;…
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