Symmetry Lines

Date: 03/30/2000 at 19:29:54
From: Ian
Subject: Symmetry lines 

How many symmetry lines are in a circle?

Date: 03/31/2000 at 18:13:58
From: Doctor Ian
Subject: Re: Symmetry lines 

Hi Ian,

I assume that you already understand that a line of symmetry is a line 
that divides a figure into two similar parts.  

Think about a circular clock. A line that goes through the 12 and the 
6 cuts the clock into two similar pieces, so that's one line of 
symmetry. 

A line that goes through the 1 and the 7 is also a line of symmetry.  

Is there at least one other line of symmetry between those two lines?  
Yes, the one that goes through the point halfway between the 12 and 
the 1, and the point halfway between the 6 and the 7. Draw a picture 
and convince yourself that this is true.  

In fact, no matter how close together two lines of symmetry are, there 
will always be another one halfway between them. 

So if you ever _thought_ that you'd counted _all_ the lines of 
symmetry, there would always be at least one more that you hadn't 
counted yet.  

What does that tell you about the number of lines of symmetry in a 
circle? 

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