Let S be a square and let S' be a square of unit area with a diagonal parallel to a side of S. Any (finite or infinite) sequence of homothetic copies of S whose total area does not exceed 4/9 can be packed translatively into S'.
The aim of the paper is to find a rectangle with the least area into which each sequence of rectangles of sides not greater than 1 with total area 1 can be packed.
If n ≥ 3, then any sequence of squares of side lengths not greater than 1 whose total area does not exceed ¼(n+1) can be on-line packed into n unit squares.
The unit square can be on-line covered with any sequence of squares whose total area is not smaller than 4.
We describe a class of boxes such that every sequence of boxes from this class of total volume smaller than or equal to 1 can be on-line packed in the unit cube.
Every sequence of positive or negative homothetic copies of a planar convex body whose total area does not exceed times the area of can be translatively packed in .
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