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AI-assisted proof of optimal packing for 11 squares

26 points bluepeter 1 hour ago 19 comments

agnishom 1 hour ago | parent

The readme has no figures :( describing the packing?

vessenes 1 hour ago | parent

I had the same thought! Pics please.

EDIT: I found it a few links down. https://jlevy.github.io/squares/cases/11.html

fredsted 1 hour ago | parent

There's a cool figure here: https://x.com/ojoshe/status/2107590622005924265

wackget 39 minutes ago | parent

Any mirrors which don't require giving clicks to neo-Twitter, please?

schiffern 32 minutes ago | parent

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

tantalor 1 hour ago | parent

Pics or it didn't happen

coppercrisp62 1 hour ago | parent

Did an interval-arithmetic branch and bound once, getting the rounding modes right took me weeks.

mlmonkey 56 minutes ago | parent

Lot more pics here: https://jlevy.github.io/squares/

WithinReason 55 minutes ago | parent

A list of many square packings, with images:

https://jlevy.github.io/squares/

aunty_helen 43 minutes ago | parent

I like geometry. These packings show there are ugly numbers, like 51.

yzydserd 26 minutes ago | parent

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

Buttons840 9 minutes ago | parent

"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. ;)

rfgplk 24 minutes ago | parent

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?

233mhz 19 minutes ago | parent

The whole point is that you can fit more than by naively stacking them...

AlexandrB 17 minutes ago | parent

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").

raincole 12 minutes ago | parent

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.

reader9274 10 minutes ago | parent

Another interesting video related to these types of problems: https://youtu.be/mVH7OPx4QZU