Okay I think I fixed the subtle little mistake.
By the way, I think this is just Wonderful!
Grrrrr there's a minor little itty-bitty mistake here somewhere, but it doesn't affect the final result. But grrrrrrr anyway, I hate it when I'm not perfect.
Here's how to get Ἀρχιμήδης's ratio
volume of inscribed sphere
---------------------------------
volume of right circular cylinder
-- one tennis ball that just fits in a cylindrical can -- with elementary integral calculus (which Ἀρχιμήδης probably knew, even though it wouldn't officially be discovered for another 1920 years).
volume of inscribed sphere
---------------------------------
volume of right circular cylinder
-- one tennis ball that just fits in a cylindrical can -- with elementary integral calculus (which Ἀρχιμήδης probably knew, even though it wouldn't officially be discovered for another 1920 years).
Find and fix my itty-bitty little mistake and ... uhhh ... I'll give you 3 slices of square no-tomato-sauce pizza.
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I BLLODY HATE THOSE BLOODY SPAM BOTS GRRR
That bloke also alledgedly invented the catapult and used mirrors to distract enemies. Pretty clever those ancient greeks
Was it Newton or Leibbnitz who came up with these integrals ? Both of them brilliant loonies, you don't get their likes these daysI think I red somewhere that Laplace (whom I only know as a scientist) or Eulaer (of whom a comic book exists in kCH) may have had their hand in there. Oh, if i only had the time.....
Hi Bob:
The substitution is incorrect in the sphere part. You can't use x^2 + y^2 = 1, because we don't know if it's 1! Instead, use x^2 + y^2 = r^2, so y^2 = r^2 - x^2, and push it through the remaining steps.
Oh No! My Brain Is Dying! I knew my body was going down the toilet, but now I see it's my Brain too!
Oh well, that's why I do these stoopid calculus problems, to keep my brain sharp. I'll have to find a harder one. Or maybe you can suggest a harder one. If I can't do it, I'll have myself institutionalized.
Grrrrrrrr.
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