Modeling Pi

Date: 01/27/2003 at 13:47:01
From: Imran
Subject: Drawing Pi on the real line

How can pi, which is irrational, be drawn on the real line?

Date: 01/27/2003 at 22:05:24
From: Doctor Ian
Subject: Re: Drawing Pi on the real line

Hi Imran,

Well, pi, like any number, is an idealization.  So if I do this, 

   ---|-----|-----|-----|*----|        * = pi
      0     1     2     3     4

then I've drawn pi on the real line. If I were to _measure_ the
distance from 0 to the '*', it wouldn't be exactly pi units, but that
doesn't matter all that much.  

For example, suppose I draw a circle, and say that the diameter is 1
unit. Then if I make a mark somewhere on the circle, the distance from 
the mark around the circle back to the mark is pi units.  

Now suppose I cut the circle at the mark, and unroll it. Then I can
label the ends 0 and pi, and I've got a number line with pi on it. 

Drawing it is a little tough using a keyboard, but you don't really
need to draw it, because you can model it.  

Find a (more or less) circular rubber band.  In _some_ units, the
diameter of this rubber band is 1.  

(Suppose it's 2.4 inches across.  If I define a 'blivet' so that 1
blivet = 2.4 inches, then the diameter of the rubber band is 1 blivet.
Does that make sense?)

Now, simply cut the rubber band somewhere, and straighten it out on a
table (without stretching it).  This is basically a number line, where
one end corresponds to zero (blivets), and the other end corresponds
to pi (blivets). 

Is that clear? 

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