Very relevant comic:
https://thejenkinscomic.wordpress.com/2024/12/01/brady-bunch...
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.
Many squares in circles bests were found this month.
Page doesn't say, but I'm guessing with help from AI
Brief search reveals prior academic research related to sexual orientation and dating apps. Doesn't appear to have done anything in maths before.
But then, why were they the first to issue the correct series of prompts to produce these results?
This would lend credence to the efficacy of using LLMs as tools. If mathematicians in the packing field had used the tool before this liberal arts student, they'd have their names on the record page.
In case you want a challenge, 11 is the smaller that has a solution that has not been proven to be optimal.
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.
Same here. Non native English speaker. The first rule is that inner squares are of size 1. Always.
Yet, in each example the inner squares shrink. Uh?
It know it was a convention to better show the arrangement, normalizing, yadda yadda.
Yet, Uh?
The total image size is scaled each time such that each solution takes up the same amount of space. It is easier to browse that way.
Would you also argue it's odd graphs don't all use the same scale as each other?
Do you want the graphs with 300 squares to be bigger than your screen, or do you want the graph with 1 square to be 30x30 px for no reason? They're just zoomed.
Some of these are wild. You expect to see something systematic, but they have little gaps between oddly placed squares in the center.
I love 130. "You thought I'm just a 2-wide strip? SIKE, here's 8-degree polynomial!"
Unrelated squares in squares, I think the interjection is PSYCH.
Both appear to be in use, the author succesfully communicated what they intended to communicate, and the audience (you) succesfully recieved the communication.
You've issued a distinction without a difference.
Awesome site. Slight peeve that arrangements with a prominent diagonal aren't all oriented in the same direction.
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