Archimedes discovered the formula many centuries before Euler, although he could not express it in modern algebraic notation.pic.twitter.com/Xc99IlwAj9
It was only 282 years ago that Euler presented in his textbooks the exact formula for the volume of a spherepic.twitter.com/10QCCtUmeA
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There's a really nice creation on Thingiverse that allows you to explore Archimedes's idea with kids:https://www.youtube.com/watch?time_continue=2&v=4VGhx99rgf4&feature=emb_logo …
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If you differentiate it w.r.t. the radius r, you get 4×pi×r^2 = surface area. Is this a coincidence?
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It's not a coincidence. Think of the volume of an onion being the same as the sum of the volumes of the layers.
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Easily provable by integrating a halfcircle and rotating by x-axis: V = integral from -r to r of π(r^2 -x^2)dx = (4πr^2)/3pic.twitter.com/LZOYaFui1n
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Not that easy when you see that Calculus was invented long time after Euler.
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Archimedes duscovered this formula. It was not Euler!
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Archimedes proved Sphere : Circumscribed Cylinder = 2 : 3 but he never wrote the formula. That π was some kind of number was alien to him. This tradition of hiding π in ratios of lengths, surfaces and volumes continued till the modern era actually. Thus I think the OP is correct
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It's a cone in a cylinder.
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Čini se da učitavanje traje već neko vrijeme.
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