Atoms as we know are the structural unit of everything. As i know that atoms are 3D objects, they have length breath and height (they have thickness).Everything is made up of atoms means everything is 3D. So why do we say that any triange ABC drawn on a piece of paper is a 2D figure?

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    $\begingroup$ Because the third dimension is too small to be considered. $\endgroup$ Oct 30, 2017 at 15:05
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    $\begingroup$ In your main question, what do you mean by second dimension? There are 3 spatial dimensions and a temporal one. $\endgroup$ Oct 30, 2017 at 15:10
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    $\begingroup$ A triangle drawn on paper is an imperfect representation of a the geometrical object triangle. $\endgroup$
    – garyp
    Oct 30, 2017 at 16:32
  • $\begingroup$ You, or anybody else, could not possibly know that elementary particles, are 3D. This is because, for an electron, we are measuring only it's electrostatic charge, and to the degree we have measured it, it follows the inverse square law. But this is something like measuring the width of my shoulders, by squeezing the clothes around them, it is not an accurate measurement of what is beneath. If you look at the literature regarding quarks & gluons, and and their interactions, you will find a different approach. The actual underlying "things", are still a mystery as regards their "width". $\endgroup$
    – user171879
    Oct 30, 2017 at 17:03

1 Answer 1


You have to make an effort of abstraction. There's no such thing as a first, second, and third dimension. To say that something has a certain number of dimension is (very roughly speaking) to answer the question "How many coordinates do I need to uniquely identify a point on this something?" Like you say, in 3D space we need 3, $x,y,z$. On a sheet of paper you can identify every point with just two numbers (think of drawing a grid of the sheet of paper). Sure the ink on the paper has some finite width, but who cares? When you say "triangle" don't think of a physical piece of something shaped like a triangle. Think of the mathematical object "triangle". Maybe it's simpler if we think circles. If you draw a circle on a sheet of paper, you might again argue that the ink has a width. But what $is$ a circle? A circle is the set of all points $x$ and $y$ such that their distance from another given point (the center) is some fixed number (the radius), i.e. $x^2+y^2=R^2$ where $R$ is the radius.

I will argue that a circle is a one dimensional object. As a matter of fact fixed the radius, you need only one number to position yourself on the circle, specifically an angle $\theta$.

enter image description here

But it makes sense doesn't it? You usually think of a line like a one dimensional object, a circle is just a line curled up a bit. What if we filled the circle and considered the inside too? That would be the set of point $x,y$ so that $x^2+y^2<R^2$. Can you see how many dimensions does this object have?

  • $\begingroup$ Its not about who 'cares' its about what's the truth. You got the point there Sure the ink on the paper has some finite width, This is exactly what i'm talking about here. you made that circle on your computer. So? what about pixels? I'm sure they also have width. All we have to do is just to zoom in alot. $\endgroup$
    – weegee
    Oct 31, 2017 at 19:07
  • $\begingroup$ And I'm sure that after zooming in, We'll reach at a point where everything has width. Even a quark will be having width, even waves and the higgs field too. $\endgroup$
    – weegee
    Oct 31, 2017 at 19:10
  • $\begingroup$ What I'm trying to say is that, like garyp said in a comment, a drawing of a geometrical figure is an imperfect representation of a mathematical object. Like you say the world is made of atoms and it makes sense to think of everything that you can see and touch as a 3 dimensional object. But this doesn't leave you unable to conceive 2D, 1D, or even 4, 5 or n D objects as a mathematical construct as I have explained. What is physically possible doesn't constrain what is mathematically possible and it still makes sense to talk about it. 1D models are of great importance in physics for example. $\endgroup$ Oct 31, 2017 at 21:25
  • $\begingroup$ You can think of a planet orbiting a star as a fundamentally 2D system for example. The planet and the star are 3D, but their configurations and trajectory happen in a plane, and this is enough to build a simple theory to predict their trajectories! $\endgroup$ Oct 31, 2017 at 21:28

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