Something I always found mind-blowing of these objects is that another way to describe them is: "you can fill them with paint, but you cannot paint the surface"
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1. Make it with transparent boxes 2. Fill with paint
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This is a similar approach to the Gabriel's Horn. Where the volume is finite but the Surface area isn't !! Math & Reality , both are fascinating.pic.twitter.com/vAylUfHtKu
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So one can fill it with a finite amount of paint but not paint the outside... Wow
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Doesn't the lower box cover part of upper box always?
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So then the first equation should say 4(...)=∞ instead of 6(...) But yeah, you right
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Not really mind blowing if you think about it the other way, if you start with an object of a given volume and divide it infinite times, the surface area will increase but the volume remains constant
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I propose the same DOES NOT APPLY TO A HOLLOW OBJECT.
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Hard to build in real life since the boxes would eventually become smaller than an atom. It's a wonder of the world of mathematics :)
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Not to mention the infinite boxes part
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is an interesting object where the side of the nth box is 1/√n. As n→+∞, the gift has infinite surface area and length but finite volume!