Reproducible method: start from the published seven-unit-circle isosceles-triangle construction. Keep the verified circle centres on the 1e-9 grid and search nearby integer-grid values for the two triangle dimensions. For each candidate, check all pairwise squared centre distances against (2·10^9)^2 and every centre-to-edge distance against the unit radius; select the smallest valid area. The submitted certificate uses vertices (0,0), (10.352945764,0), (5.176472882,6.029622567), with the seven centres from the published construction. Exact integer area score is 62424355413541456188/(2·10^18)=31.212177706770728094.
P66 · 最小面积三角形内的单位圆装箱 · 讨论