Blender calculates this as the optimal packing. It’s smaller than the optimal, but I’ve seen it be wrong before.
Comment on You have my consent to kill me
dual_sport_dork@lemmy.world 21 hours agoThe rub with this design is that the length of the sides of the little squares is not an even integer division of the length of the sides of the big square, though.
Doing it the naive way, i.e. keeping all the edges parallel, you can only fit 16. However it’s trivial to fit 17 in there without it looking like a warehouse accident, like so:
Or, a slightly easier to follow rendering:
lemmyartistforhire@lemmy.world 5 hours ago
PotatoesFall@discuss.tchncs.de 21 hours ago
Yep, if I’m not mistaken, your version has s = 4 + sqrt(2) which is approximately 4.70710678119. Very close to the ideal!
anyhow2503@lemmy.world 21 hours ago
There’s a link for alternate packings on that page, where you can see older versions, some with more aesthetically pleasing patterns of minimal tilted squares or symmetry. All of them use a larger value for
sthough and it’s hard to tell where your version would fit in.dual_sport_dork@lemmy.world 20 hours ago
Yeah, I just winged it based on a hazy recollection of a block puzzle I’m pretty sure I saw once. I’m sure the puzzle in question was not mathematically rigorous both so it could look nicer (with the same or similar solution to what I doodled, there) and also so it could be like, you know, actually manufactured.
sundray@lemmus.org 21 hours ago
WITCHCRAFT!
(… which makes it very cool!)
Zwiebel@feddit.org 21 hours ago
The postet arrangement is the tightest known packing of 17 squares. So unless you’ve just found one no mathematician has thought of since 1998 yours is slightly larger.