its like when you google if theres a logical xnor operator because you forget that == is a thing for Booleans Too
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im so glad my lecturers look past my inexplicable madness and are my biggest hypemen because their reccomendations probably carry the fuck out of me like if you tell it how it is universities would not take my ass. never speaks, is constantly moving around and squirming, will not do work under direct supervision like straight up if they took me in for an interview i mightve been cooked
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Graphical proof is ugly and boring so calculus
Volume of a cube is l*w*h
The number of blocks needed to build the frame is 4(l+w+h)=k
Letâs just say k=4
V=w*h*(1-w-h)=wh-w^2h-wh^2
To find extrema, take partial derivatives with respect to each and set to zero
dV/dw=h-2wh-h^2=0
dV/dh=w-w^2-2wh=0
w=1/3 h=1/3 therefore l=1/3
Generally maximal volume is always a cube so you can cheat lots of optimisation problems this way
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I looked at it and was like âactually thatâs too annoying to see where the maximum wasâ so I also judged graphical proofs it seems
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i saw what was potentially a proof for Squares done with calculus but i dont actually know what calculus is and given it was made by John Calculus after he put an entire apple in his cheek like a chipmunk i dont think i want to know
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can you repeat the proof with a harder number for k because my mind immediately figured it out and now i donât wanna look at it
can everyone here do math but me
dV/dw=k/4*h-2wh-h^2=0
dV/dh=k/4*w-w^2-2wh=0
w=k/12 h=k/12 l=k/12
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4(l+w+h)=4 is just 4 divided by 3
thats not meant to be a diss i just feel like im in shapes and colors class and yall are squaring the circle
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Atlas has been converted like in forum mafia
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Everyone in my calc classes always hates optimisation and I donât get it. So youâre certainly not alone
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musi Manka is actually slightly different here because you reuse blocks on the corners
And you canât have fractional blocks
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 itâs 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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thereâs 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 â1â, 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) doesnât really equal 1, mathematicians say it does because theyâre a bunch of nerds who donât want to redo their work when they realise they made an error (this comes up a lot)
thatâs the simpliest way to do the problem, and is also not very fun