Packing unit squares in a square $s(27)$
The side of the smallest square into which $27$ unit squares can be packed.
Lower bound:
$2\sqrt{2}+\frac{27+2\sqrt{10}}{13}$
(≈5.391854)
Upper bound:
$5+\frac{1}{\sqrt{2}}$
(≈5.707107)
Updates
-
Lower bound: $2\sqrt{2}+\frac{27+2\sqrt{10}}{13}$
(≈5.391854)
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14] -
1979
Upper bound: $5+\frac{1}{\sqrt{2}}$
(≈5.707107)
F. Göbel, Geometrical Packing and Covering Problems, in Packing and Covering in Combinatorics, A. Schrijver (ed.), Math Centrum Tracts 106 (1979) 179-199.
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14]