Packing a convex domain with similar convex domains

Given a convex domain C and a positive integer k, inscribe k nonoverlapping convex domains into C, all of them similar to C. Denote by f(k) the maximal sum of their circumferences. In this paper it is shown, that for C square, parallelogram or triangle (1) the first increase of f(k) after k = l2 occurs not later than at k = l2 + 2, (2) constructions can be given, where the following lower bounds are attained for f(k) = f(l2 + j): (1c) ⩾ l + (j − 1)2l j odd, l⩾ 2⩾ l + j2(l + 1) jeven, l⩾2 where c denotes the circumference of C.