HN Explorer

13 comments

[ 1.7 ms ] story [ 38.9 ms ] thread
gus_massa
In case you want a challenge, 11 is the smaller that has a solution that has not been proven to be optimal.
sestep
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.
razorbeamz
Looks like Hiroshi Nagamochi did all the boring work.
NooneAtAll3
I love 130. "You thought I'm just a 2-wide strip? SIKE, here's 8-degree polynomial!"
npodbielski
Why 4 is trivial but 6 had to be proved?
amne
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.

bradley13
Some of these are wild. You expect to see something systematic, but they have little gaps between oddly placed squares in the center.
matthewfelgate
Sometimes nature is beautiful and sometimes it isn't.
xnx
Awesome site. Slight peeve that arrangements with a prominent diagonal aren't all oriented in the same direction.