= Alternating-radius square circle packing
{title2=$\eta=\pi(r_1^2+r_2^2)/(2d^2)$}
Place equal numbers of radii $r_1,r_2$ on alternating sites of a square nearest-neighbour lattice of spacing $d$. Nonoverlap requires $d\ge\max(r_1+r_2,\sqrt2r_1,\sqrt2r_2)$. A two-circle cell has area $2d^2$, giving the displayed <packing fraction>. Its maximum within this geometry occurs at large-to-small radius ratio $1+\sqrt2$ and is $\pi(1-1/\sqrt2)$; smaller interstitial circles leave unused space, while larger ones force the large-circle lattice apart.
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