thats awesome i dont understand how 4 divided by 3 gets us here
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okay but im sick at greater and less than
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So for a given number of blocks the dimensions of the optimal solution will vary slightly. But those are marginal cases, in practice it’s still gonna be pretty close to a cube. But it would be an interesting optimisation to make
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i got grilled for a teacher in high school because i didnt get their names and as a result could not say which one was needed in my head i call them < and >
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its. its the crocodile. the crocodile eats the bigger fish. They are the same symbol
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there’s a four on both ends so the answer has to be a decimal beginning with 1. you can divide 4 by itself on both ends to get “1”, because removing the same amount on each side of an = problem will result in the same problem
so (l+w+h)=1
which the answer to has to be 0.33333, because whilst 0.9999999999999999(etc) doesn’t really equal 1, mathematicians say it does because they’re a bunch of nerds who don’t want to redo their work when they realise they made an error (this comes up a lot)
that’s the simpliest way to do the problem, and is also not very fun
yeah
NYAAAAAAAAAAAAAAAAA calculus 
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calculus is fine but it’s the boring way to do the problem tbthtbhtbhtbthbtbthbt
removes the JOY and WHIMSY from solving them without it
ok so
i get all of the individual parts. They make lots of sense in my brain. Those are things that compute. They do not fit together
I think this is something I need to just slot into my pondering time because i just dont click sometimes. like my mermeory
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If you increase the starting perimeter then the l w h just change proportionally. I think the clearer thing to do would be to set k=1 so you learn all the dimensions as fractions of your total number of blocks
What joyful and whimsical method would you recommend? Number theory?
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It’s a calc problem of course I’m gonna do calc
i am at 7x10x10
i. uh. dont actually know what to do with that information now that i think about it
i spend all week being forced to do math and am excited to go to fol on the weekends and talk to people
everyone else on this forum spent the whole week being forced to talk to people and go to fol on the weekends to do math
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Oh you have no fucking idea how true this is
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The lore is Bad
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I think an argument without calculus should be
Suppose the optimal solution was not a cube. Then the length and width (or height, but we can assume it’s not the height without loss of generality) are not equal. Again without loss of generality, we can assume the length is lower than the width.
Increasing the length by x and decreasing the width by x leaves the overall number of blocks of the frame unchanged, but has increased your volume, since (length + x)(width - x) - length * width = x*width - x*length - x^2 = x(width - length - x) > 0 as long as x < (width - length).
It occurs to me now that if you are restricted to integers then maybe the optimal solution can’t be a cube though thbthbthtbhbhtbt
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