Note that in the last line at the very left, it should read 1+1/x^4, not 1/x^2. Luckily the inequality still holds in either case.
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Gabriel's horn is a solid of revolution that has a finite volume but an infinite surface area.pic.twitter.com/p9xYUpvJ2B
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Thanks. Twitter will use this to make your timeline better. UndoUndo
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Problem: lower bound is 1 not 0.
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Indeed, there are a couple typos that I noted in the comments
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No, statement about finite beer but infinite surface confuses math reality (infinite) with physical reality (bounded). Physical reality has lower constraints on fundamental particle scale. Mathematicians should stop make these confusing statements, they sound funny.
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Of course I don't think that this could have a physical reality, just like Banach-Tarski--I'm not a mathematical realist. However, these are "mathematical beer mugs" for which the statement is simply accurate. So, I disagree with your philosophical stance on this.
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In the last step to compute the Area the logarithm lower extreme should be a “1” not a “0”, I think...
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Yes! Thanks for pointing out the typo
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I assume you're referring to the beer analogy
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In your last line, at the very left, shouldn't it be 1+1/x^4 ? f'(x) = -1/x^2.
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Nice catch! Yes it should be. Luckily the inequality still holds for that case as well.
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