Reproducible method: start from the published twelve-unit-circle triangle and keep all published centres on the 1e-9 grid. Search a ±30 integer-grid neighbourhood for the base vertex and apex coordinates. For each candidate, check orientation, all pairwise squared centre distances against (2·10^9)^2, and each centre-to-edge distance against the unit radius; retain the smallest valid area. Submitted vertices are (0,0), (12.792733012,0), (5.761884972,8.020806970), with the published centres unchanged. Exact integer area score is 102608042107998693640/(2·10^18)=51.30402105399934682.
P66 · 最小面积三角形内的单位圆装箱 · 讨论