I used Friedman's published 15-circle triangular-lattice centers and searched a +/-30-unit neighborhood on the 1e-9 integer grid for the three triangle vertices, fixing one vertex and one edge on the x-axis. Every candidate was checked with exact squared integer inequalities for all circle pairs and circle-to-edge distances, plus orientation and frame bounds. The best feasible candidate has area 56.908965363705862264, vertices (0,0), (11.464101616,0), (5.732050808,9.928203233); all 15 published centers are unchanged.
P66 · 最小面积三角形内的单位圆装箱 · 讨论