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Is paper 2D or 3D?

## Is paper 2D or 3D?

[From: Mathematics] [author: ] [Date: 01-07] [Hit: ]
Is paper 2D or 3D?......

Is paper 2D or 3D?

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JG say: Technically-speaking it IS 3-D. Paper has a thickness. Any object drawn or printed on it is 2-D.
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lenpol7 say: paper is 3D . It has width , length and a very thin thickness.
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oldprof say: 3D, paper has thickness no matter how tiny.

If we project an image onto that paper the image is 2D as it has no thickness.
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Jeffrey K say: A sheet of paper is a thin 3D object. But the surface of a paper that you write on is 2D.
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Iggy Rocko say: 3D
Paper's thickness is small but > 0.
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Krishnamurthy say: Paper 2D. Paper 2D in Unreal Engine 4 (UE4) is a sprite-based system for creating 2D and 2D/3D hybrid games entirely within the editor. At the core of Paper 2D are Sprites (which are a Texture Mapped Planar Mesh and associated Material).
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no sea nabo say: paper = 3D
a drawing = 2D
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oyubir say: That is your modelization choice.

If you look with a microscope, you'll see that its surface is not plane at all. There are lots of bumps. And each of this bumps, when you zoom in, are not smooth neither. Their own surface is made of lots of bumps. Which themselves, etc, etc.
In other words, surface of a paper (as everything else) is fractal.
So, you may also say that its dimension is more than 2, but less than 3 (see "fractal dimension" on wiki for more about non integer dimension).

And I am pretty sure a physicist adept of string theory could be even more a pain in the a... that I am, by saying that the paper is 17D or so...

The point is, real life is not mathematical. We use mathematics to modelize real life. So, the paper is not 2D or 3D, or anyD. It is its mathematical model that is once of those. And when we modelize the paper, we have arbitrary choice to make. Depending on what you want to do and to predict with your model.

If, as Elaine said, you want to look at what you can draw on it, most reasonable choice is to consider it 2D.

If, as Steve said, what you want to do with your mathematical model is compute how many sheet of paper you can store in your drawer, then you have to consider it 3D.

If, as I said with microscopes, what you want is to compute the amount of information needed to reproduce its shape (it is infinity, but how big is this infinity?), you have to consider fractal dimension (well, one may say, Planck is here to spare us this consideration, since in reality, you can't zoom for ever, and therefore, paper is not really fractal).

And if you consider your paper as a shape in a multiverse of string theory, then you need whatever dimension string theorist say there are nowadays...

So, real question is more: why to you want to know? For which purpose? It is answer to this question that will say which is the best dimension for you. There is no "real" answer to this question. Reality is not mathematical; dimension is.
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Elaine M say: Looking at something on it is 2D, paper itself is 3D
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Steve A say: 3D. You can easily see this if you have a stack of it. The surface we normally write on is 2D.
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JG say: Technically-speaking it IS 3-D. Paper has a thickness. Any object drawn or printed on it is 2-D.
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khalil say: in fact, the paper sheet is 2D but you may imagine 3D.
in this photo, you see the windows are further to you.
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