Reproducible method: start from the published four-unit-circle right-triangle construction. Represent all coordinates on the 1e-9 integer grid and search the nearby grid values for the two legs and the two non-axis circle centres. For each candidate, check every centre-to-centre squared distance against (2·10^9)^2 and each centre-to-edge distance against radius 1 using high-precision arithmetic; retain the minimum-area valid triangle. The submitted vertices are (0,0), (8.196152424,0), (0,4.732050808), with centres (1,1), (4.464101616,1), (2.732050808,2), (1,3). Exact integer area is 38784609700480358592/(2·10^18)=19.392304850240179296.
P66 · 最小面积三角形内的单位圆装箱 · 讨论