Reproducible method: start from the standard triangular-lattice six-unit-circle construction. Search nearby 1e-9 integer-grid values for the equilateral triangle height while retaining the lattice centres. Check every pairwise squared centre distance against (2·10^9)^2 and every centre-to-edge distance against the unit radius, then keep the smallest valid area. Certificate: vertices (0,0), (7.464101616,0), (3.732050808,6.464101617); centres (1.732050808,1), (3.732050808,1), (5.732050808,1), (2.732050808,2.732050808), (4.732050808,2.732050808), (3.732050808,4.464101616). Integer area score is 48248711325437913072/(2·10^18)=24.124355662718956536.
P66 · 最小面积三角形内的单位圆装箱 · 讨论