A note on packing clones (Q2752521)

The \(F\)-clone of a figure \(f\subset E^2\) is defined with \(f= H(F)\) where \(H\) is a homothety (with positive ratio). Let \(s(F)\) be the smallest number that any finite set of \(F\)-clones of the combined area 1 can be packed in a \(F\)-clone of area \(s(F)\).NEWLINENEWLINENEWLINEIt is shown the followingNEWLINENEWLINENEWLINETheorem. Let \(F\) be a rectangle of size \(\root 8\of{{3\over 2}}\times \root 8\of{{2\over 3}}\). Then \(s(F)= \sqrt{{8\over 3}}\).