For some reason, I always loved this formula
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What other formulas you love?
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Archimedes knew that the volume of a sphere is 2/3 the volume of a circumscribed cylinder. He had them engraved on his tombstone.pic.twitter.com/quBLKg7M08
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It's even nicer when, like Archimedes, you consider the cone, the cylinder and the sphere to get the 1:2:3 ratio for their volumes.https://twitter.com/aperiodical/status/1148864617692704769?s=19 …
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The Limit of a Riemann Sum (aka definite integral) saves the daypic.twitter.com/Q4gS7JpDHK
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Perfect visual proof
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It was only around 225 BCE that Ἀρχιμήδης (Archimedes) published Περὶ σφαίρας καὶ κυλίνδρου (On the Sphere and Cylinder), where he proved the volume of a sphere to be ⅔ of the one of the circumscribed cylinder, effectively giving the same formula almost 2000 years earlier
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Euler di many fantastic things of maths, but I don’t understand why you give him credit for the volume of the sphere. He would clearly not have claimed credit for this himself.
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This must be much harder than it looks. How did Archimedes not find it, and failing that, how did Fermat or Newton not get it?
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I also wondered that, and on looking at https://en.wikipedia.org/wiki/Sphere#Enclosed_volume … decided that
@fermatslibrary's tweet was badly worded. On Archimedes there is also this: https://en.wikipedia.org/wiki/On_the_Sphere_and_Cylinder … - 8 more replies
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