The 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:
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.
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 s though and it’s hard to tell where your version would fit in.
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.
dual_sport_dork@lemmy.world 2 months ago
The 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:
Image
Or, a slightly easier to follow rendering:
Image
Zwiebel@feddit.org 2 months 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.
PotatoesFall@discuss.tchncs.de 2 months 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 2 months 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 2 months 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.
lemmyartistforhire@lemmy.world 2 months ago
Image
Blender calculates this as the optimal packing. It’s smaller than the optimal, but I’ve seen it be wrong before.
sundray@lemmus.org 2 months ago
WITCHCRAFT!
(… which makes it very cool!)