Every sequence of positive or negative homothetic copies of a planar convex body $C$ whose total area does not exceed $0.175$ times the area of $C$ can be translatively packed in $C$.
@article{116925,
author = {Janusz Januszewski},
title = {Translative packing of a convex body by sequences of its homothetic copies},
journal = {Archivum Mathematicum},
volume = {044},
year = {2008},
pages = {89-92},
zbl = {1212.52020},
mrnumber = {2432845},
language = {en},
url = {http://dml.mathdoc.fr/item/116925}
}
Januszewski, Janusz. Translative packing of a convex body by sequences of its homothetic copies. Archivum Mathematicum, Tome 044 (2008) pp. 89-92. http://gdmltest.u-ga.fr/item/116925/
Finite packing and covering, Cambridge Tracts in Mathematics, Cambridge University Press, Cambridge 154 (2004). (2004) | MR 2078625 | Zbl 1061.52011
A note on translative packing a triangle by sequences of its homothetic copies, Period. Math. Hungar. 52 (2) (2006), 27–30. (2006) | Article | MR 2265648 | Zbl 1127.52023
Translative packing of a convex body by sequences of its positive homothetic copies, Acta Math. Hungar. 117 (4) (2007), 349–360. (2007) | Article | MR 2357419 | Zbl 1174.52010
Approximation of convex bodies by rectangles, Geom. Dedicata 47 (1993), 111–117. (1993) | Article | MR 1230108 | Zbl 0779.52007
On packing of squares and cubes, J. Combin. Theory 5 (1968), 126–134. (1968) | Article | MR 0229142
Some packing and covering theorems, Colloq. Math. 17 (1967), 103–110. (1967) | MR 0215197 | Zbl 0152.39502
A note on packing clones, Geombinatorics 11 (1) (2001), 29–30. (2001) | MR 1837580 | Zbl 1005.52010