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### Is a Circle a Polygon?

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

Is a circle a polygon?

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

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/
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Associated Topics:
High School Conic Sections/Circles
High School Definitions
High School Geometry
High School Triangles and Other Polygons
Middle School Conic Sections/Circles
Middle School Definitions
Middle School Geometry
Middle School Triangles and Other Polygons

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