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December 12th, 2016, 05:38 AM   #1
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Are 3D shapes layered 2D shapes?

Today at math class, our teacher was using pages and a book to depict how 2d objects make 3d objects. Many '2d' pages stacked on top of each other added a height dimension. I had a question. The paper was really 3d, it had a really, really, small height, which eventually added up to a visible one when many were stacked upon one another. A real 2d object would have a height of 0. So, 0 + 0 + 0... = 0! Which means that even an infinite number of 2d objects cannot stack up! My teacher told me to figure it out.

I know that the statement '2d objects can stack up to make a 3d object' is true, it is used in thought experiments like Flatland.

So, I'm confused. I'm just in 8th grade, and I'm not that great at math, but I have a feeling that this has something to do with calculus. I've seen a few things using zeros, like the instantaneous velocity thing (0/0) and a few others that have been solved with calculus.

It would be great if someone could gimme a solution. Also, if it does have something to do with Calculus, please try to explain it as simple as possible, so an 8th grader could understand .

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December 12th, 2016, 08:57 AM   #2
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The concept you're missing does come from calculus as is known as the "differential"

The differential is basically a number greater than 0 that gets infinitely small.

The idea is that your 2D layers are of differential thickness. They do stack and provide a real thickness. Calculus is basically the study of what happens when you let differentials truly tend towards 0.

I'll probably get flamed for this non-rigorous explanation but it's a start anyway.

Last edited by romsek; December 12th, 2016 at 09:49 AM.
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December 12th, 2016, 09:39 AM   #3
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volumes formed by similar cross sections
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