A well-known open problem of Meir and Moser asks if the squares of sidelength 1/n for can be packed perfectly into a rectangle of area . In this paper we show that for any , and any that is sufficiently large depending on t, the squares of sidelength for can be packed perfectly into a square of area . This was previously known (if one packs a rectangle instead of a square) for (in which case one can take ).
Keywords: Harmonic series; Meir–Moser problem; Square packing.
© The Author(s) 2023.