"God is dead and the optimal packing of squares killed him." I will never not think of this meme when looking at these horrors. I see it, but I don't like it. ;)
Isn't this obvious? Why do you need a proof for it, just stack the cubes next to each other? If we're talking infinitesimally thin squares, then stack them on top of each other? Am I missing something?
Look at some of the other links people have posted for optimal packings. The optimal 11 square packing looks nothing like what you're describing ("just stack the cubes next to each other").
fwiw The prime site for square in square packing is at https://kingbird.myphotos.cc/packing/squares_in_squares.html
The triangular view is most interesting. And a 20 minute video on this view is at https://youtu.be/uL5wuiy34rs
"God is dead and the optimal packing of squares killed him." I will never not think of this meme when looking at these horrors. I see it, but I don't like it. ;)
More background on Walter Trump's 11-squares packing:
https://vplevris.medium.com/eleven-squares-one-tiny-gap-and-...
https://en.wikipedia.org/wiki/Walter_Trump
https://x.com/fermatslibrary/status/2032179976028475737
More on the new proof:
https://startupfortune.com/ai-models-formally-proved-walter-...
https://jlevy.github.io/squares/cases/11.html
The readme has no figures :( describing the packing?
There's a cool figure here: https://x.com/ojoshe/status/2107590622005924265
Any mirrors which don't require giving clicks to neo-Twitter, please?
https://kingbird.myphotos.cc/packing/squares_in_squares.html
For more packings (circles in circles, etc) check out this page: https://erich-friedman.github.io/packing/index.html
Pics or it didn't happen
I had the same thought! Pics please.
EDIT: I found it a few links down. https://jlevy.github.io/squares/cases/11.html
<https://en.wikipedia.org/wiki/File:Packing_11_unit_squares_i...> from https://en.wikipedia.org/wiki/Square_packing
A list of many square packings, with images:
https://jlevy.github.io/squares/
I like geometry. These packings show there are ugly numbers, like 51.
Lot more pics here: https://jlevy.github.io/squares/
Another interesting video related to these types of problems: https://youtu.be/mVH7OPx4QZU
Did an interval-arithmetic branch and bound once, getting the rounding modes right took me weeks.
Isn't this obvious? Why do you need a proof for it, just stack the cubes next to each other? If we're talking infinitesimally thin squares, then stack them on top of each other? Am I missing something?
It takes less time for you to try to read about the question than to type this comment. I know the link doesn't contain visualization, but... come on.
The whole point is that you can fit more than by naively stacking them...
Look at some of the other links people have posted for optimal packings. The optimal 11 square packing looks nothing like what you're describing ("just stack the cubes next to each other").