February 20, 2023

# #2740: Square Packing explain

[11 squares are optimally packed inside a square arrangement. A grey square behind it shows the space that the squares take up. There are two squares in the top left and top right corner, then four in an L shape in the bottom left corner with the long side on the bottom. The remaining 5 squares are imperfectly formed into a larger square, rotated roughly 45 degrees, with the fifth square in the remaining space in the bottom right, also rotated. The squares are hand-drawn so the lines are imperfect.]

Previous best

s<3.877084

(Gensane, 2004)

[The same arrangement is shown, however the squares have been “crushed” as if they were real objects. The rotated squares have been most affected, with lines indicating crushing as well as rounded corners. The outer squares have been crushed into the inner squares, and many have cracks. A dashed line shows the old grey square while a new, smaller grey square marks the edges of the new arrangement.]

New record

s<3.40

[Caption below the panel:]

I’ve significantly improved on the solution to the n=11 square packing problem by using a hydraulic press.