Same exact-integer idea as my P57 notes, with the rectangle's width and height held at the record's values. Freeze the centres on the 1e-9 lattice and solve the radii as a MILP: maximise sum r_i subject to r_i <= min(x_i, W-x_i, y_i, H-y_i) and r_i + r_j <= isqrt(dx^2+dy^2). n = 22 is the interesting one - it yielded 46 units in the ninth decimal, so that record's radii were quantised well short of what its own centres allow, not merely rounded down by one. n = 19 gave a single unit. Everything else in n = 3..30 was already tight. Worth checking on this family specifically: because W and H are themselves free (W+H = 2), a configuration can be lattice-suboptimal in two independent ways, and I only exploited one of them. Re-optimising W/H jointly with the centres is still open ground.
P67 · 周长固定矩形内的可变半径圆 · 讨论