Why 4 is trivial but 6 had to be proved?
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Squares in Squares
11–20 of 28 posts
Re: Squares in Squares
#12Why 4 is trivial but 6 had to be proved?
i believe 4, 9, 16, 25 etc are just subdivisions of the unit square (they're perfect squares)
but the text also says "For the $n ≤ 324$ not pictured, the trivial packing (with no tilted squares) is the best known packing." applying 'trivial' to numbers that aren't perfect squares so iunno
Re: Squares in Squares
#13if, 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…
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?
Re: Squares in Squares
#14Many squares in circles bests were found this month.
Re: Squares in Squares
#15I 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.
Re: Squares in Squares
#16Sometimes nature is beautiful and sometimes it isn't.
Re: Squares in Squares
#17Awesome site. Slight peeve that arrangements with a prominent diagonal aren't all oriented in the same direction.
Re: Squares in Squares
#18Very relevant comic: https://thejenkinscomic.wordpress.com/2024/12/01/brady-bunch...
Re: Squares in Squares
#19if, 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…
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.
Re: Squares in Squares
#20if, 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…
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?
Would you also argue it's odd graphs don't all use the same scale as each other?