One Dimension

Date: 05/13/2003 at 16:29:30
From: Emma
Subject: Is there such thing as 1D?

My question is about 1D (one dimension). I have been wondering if 
there is such thing as 1D, because if you draw a line, it has a length 
and a very small width. If you draw a dot, it has a small length and 
width. Does this mean there is no such thing as 1D?

Date: 05/13/2003 at 22:20:00
From: Doctor Peterson
Subject: Re: Is there such thing as 1D?

Hi, Emma.

You're right: in the real world, everything is made of atoms, which 
are three-dimensional, so nothing we see is one- or two-dimensional. 
Everything has some thickness.

But in mathematics, we can imagine and study such objects (lines, 
planes, circles, and so on); and we use those imaginary objects to 
model the real world. For example, we learn in math how to find the 
area of a rectangle; then we can measure a wall and treat its surface 
as a rectangle. That allows us to find its area and decide how much 
paint we need, even though the layer of paint will have some thickness 
and will not actually be an exact rectangle in the mathematical sense.

So although what we study in math doesn't really exist as a physical 
object, it is close enough to real objects to be useful.

And when we make geometrical drawings, we are not making actual lines 
and circles, but pictures of lines and circles that really exist only 
in our imagination. So we ignore the thickness of the things we draw, 
and just think about what we mean by those drawings: lines that have 
no thickness and points that have no size.

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/