Gabriel's Horn Paradox

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How can an infinitely long shape have a finite volume, but infinite surface area? Answers on a postcard please to the usual address.

Here's a rigorous mathematical proof from Numberphile. The best bit is right at the end when the paradox flummoxes the mathematician who shows how the paradox works.

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Here's a conceptual explanation from Up and Atom that's much easier to understand. Interestingly, Jade reckons there's no paradox, because comparing volume with surface area is not the same thing. I'm not sure that I completely agree with that, but I can see where she's coming from. Watch the video and let us know what you think.

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This is for those with long attention spans who understand all the squiggly maths.
 
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