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amne 25 minutes ago [-]
if, like me, you're a non-native english and speaker don't immediately understand what this is about: the page shows for each `n` what's the minimum `s` such that `n` squares with side of length 1 fit in a square with side of length `s`.
what I'm curious about though is what a proof for something like this looks like. and why does it need a proof? not to mention the randomness of some of the `n`s. Math is most of the time beatiful and whenever I see something like `n=11` I think "it looks wrong so it must be wrong" yet it has a proof.
sestep 5 hours ago [-]
The triangular table view is fascinating. It looks like the periodic table. I wonder if there are number-theoretic lemmas (or at least conjectures?) about what "family" the optimal packing for a given number falls into (like diamond, diagonal strip, two blobs, etc). I didn't see anything when skimming the survey paper linked at the bottom of the site, but I'm sure there's a lot more literature here.
gus_massa 1 days ago [-]
In case you want a challenge, 11 is the smaller that has a solution that has not been proven to be optimal.
npodbielski 35 minutes ago [-]
Why 4 is trivial but 6 had to be proved?
NooneAtAll3 3 hours ago [-]
I love 130. "You thought I'm just a 2-wide strip? SIKE, here's 8-degree polynomial!"
razorbeamz 4 hours ago [-]
Looks like Hiroshi Nagamochi did all the boring work.
what I'm curious about though is what a proof for something like this looks like. and why does it need a proof? not to mention the randomness of some of the `n`s. Math is most of the time beatiful and whenever I see something like `n=11` I think "it looks wrong so it must be wrong" yet it has a proof.