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2D surfaces in the third dimension?

  1. Jul 13, 2010 #1

    I just need to know whether or not surfaces with zero size in the third dimension, 6x8x0, is considered two-dimensional.

    The surface is there all the time. It has a location in the third dimension, so wouldn't it be a 3D object? I am not sure whether I should call a flat surface (as if a monitor could possibly be completely flat) 2D or not.

    The material it is the surface of (this surface doesn't have any matter, of course) is 4D.

    If I ask someone to point at a 2D surface, and they point at a monitor or any other flat surface (they are not exactly smart, they don't think a round ball would be accepted because it's not flat. Nothing is really flat, you'd need to cut out a really small point), do I tell them:

    "Correct, the surface has no size in the third dimension" or do I tell them "Incorrect, it has a location in the third dimension"?

    Can a 2D object have a location in the third dimension?

  2. jcsd
  3. Jul 13, 2010 #2
    A good way to think of it is to consider how many coordinates you need to describe it. The surface it self has a location in all three dimensions, so you need three coordinates to describe it. However, if you consider a point on the surface you only need two coordinates (that is two dimensions) to describe it. Of course the catch is that by requiring the point to be on the surface you are in effect giving the third coordinate.
  4. Jul 14, 2010 #3
    IMO a dimension is a mathematical concept, not a concrete reality.

    Objects in our world have as many dimensions as one feels necessary to describe their properties and behaviours.
    A table is two dimensional when it suits us to say it is. When we want to get it through a doorway, suddenly it's three dimensional.

    Some lunatics think it has as many as eleven. Not my problem.
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