Archimedes discovered the formula many centuries before Euler, although he could not express it in modern algebraic notation.pic.twitter.com/Xc99IlwAj9
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Archimedes discovered the formula many centuries before Euler, although he could not express it in modern algebraic notation.pic.twitter.com/Xc99IlwAj9
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 …
If you differentiate it w.r.t. the radius r, you get 4×pi×r^2 = surface area. Is this a coincidence?
It's not a coincidence. Think of the volume of an onion being the same as the sum of the volumes of the layers.
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
Not that easy when you see that Calculus was invented long time after Euler.
I've written about this, but was going to write a blog post aimed at a general reader. When I do so, would you be interested?
Archimedes duscovered this formula. It was not Euler!
Sofisticado dms guigui
creio que facilmente uma integral tripla demonstra isso, hehehe
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