A New Lower Bound for Packing 17 Unit Squares
Another better lower bound for n=17 square packing
Gustavo Massaccesi improves the lower bound for packing 17 unit squares into a larger square, proving s(17) ≥ 4.5058. Building on recent work by Sam Burns, he uses linear programming to find optimal weight distributions, reducing the gap between known lower and upper bounds. The result, verified by a rational arithmetic program, also improves bounds for s(18), s(19), and s(20).
So if we try to fit 17 unit squares there, at least two unit squares must share one of the 16 interesting points.
- dooglius
Responding to a couple comments here: there is no picture or new arrangement of squares because those are _upper_ bounds for the problem. The best known arrangement, i.e. the best known upper bound, has not changed.
- scuppernong
Some of these point arrangements superficially resemble Chladni figures (https://chalkdustmagazine.com/regulars/on-the-cover/cover-ch...) coming from the vibrations of a square drum.
Orthogonally, I wonder if these arrangements are generalizable to give lower bounds for N = n^2 + 1
- teddyh
None of the images has any squares.