It's a gift that's easy to store, but problematic to wrap.
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You can fill it with paint, but you can’t paint it.
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Again, not quite. You're thinking about pouring it down the top, but that wouldn't work since it has infinite length (sum from n=1 to infinity of 1/√n is divergent). In fact, inserting paint at any finite point and letting it fall wouldn't work - it'd be falling forever!
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About the surface... One face isn't the same as the other ones and is 1/n^2 - 1/(n+1)^2
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Does this equal phi squared? Looks like a rounding error’s difference....
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I think if the pyramid is constructed by cubes whose sides are 1/Pn where Pn is the nth prime we end up having a finite object with fine volume, area and length.
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Interesting. Find it difficult wraping my head around Gabriel's Horn: Finite volume, infinite surface area! I've always suspected that despite our progress in science, engg, and tech, our understanding of infinity (and even zero) may be abysmally wrong.https://twitter.com/ravicha47372787/status/1209750284781514752?s=20 …
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This 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!
Learn more about this interesting paradox here: