Is a Circle a Polygon?

Date: 03/07/99 at 21:25:33
From: Tyler Coffman
Subject: Is a circle a polygon? 

Is a circle a polygon?

Please help me.

Date: 03/08/99 at 09:00:26
From: Doctor Peterson
Subject: Re: Is a circle a polygon? 

Here are some answers in the Dr. Math archives about this question:

   Can a Circle be a Polygon?
   http://mathforum.org/library/drmath/view/54816.html   

   Polygons, Infinite Sides, and Circles
   http://mathforum.org/library/drmath/view/54912.html   

   Polygons and Circles
   http://mathforum.org/library/drmath/view/57723.html   

The first does not really quite deal with the question, but the second 
is more or less the answer I would give, explaining the concept of a 
"limit." The third leaves it open, saying mathematicians disagree. You 
should look through all of these to get different perspectives.

Here is the simple answer: no, a circle is not a polygon. A polygon is 
composed of a finite set of straight line segments, and a circle is 
not. But you can make a polygon that is as close to a circle as you 
want; the more sides you give it, the more it will look like a circle. 
In fact, the other day a student asked if we could show him what a 
"googolgon" looks like (a polygon with a "googol" of sides, meaning 10 
to the 100th power!). I said I can't make one, but if he looks at a 
circle he will see what a googolgon looks like as accurately as I could 
draw one! The sides of a googolgon would be smaller than atoms, so if I 
tried to draw it, it would look no different from a circle. That is 
what we mean when we say that a circle is in some sense an "infinite 
polygon" or "the limit of a sequence of polygons": it is not a polygon, 
but you cannot tell the difference between a circle and a sufficiently 
big polygon. And where mathematicians might disagree is simply in their 
willingness to talk about infinity as if it were a real number, and to 
leave out careful words like "limit."

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