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### Circumference vs. Perimeter

```Date: 05/09/2003 at 12:01:23
From: Todd
Subject: Circumference vs. Perimeter

Technically speaking, can the term "perimeter" apply to a circle in a
mathematical context?

While I would never actually refer to the circumference of a circle
as its "perimeter," a discussion recently arose about whether the
term "perimeter" can even APPLY to a circle. I consulted a standard
dictionary, which said it was the length of a closed curve enclosing
an area, so it would seem to apply under that definition. A
mathematics dictionary said that perimeter was the sum of the lengths
of the edges of a closed figure, but since a circle has no edges,
this doesn't seem to apply to circles. However, the same mathematical
dictionary defined circumference as "the perimeter of a circle."
```

```
Date: 05/09/2003 at 12:34:15
From: Doctor Peterson
Subject: Re: Circumference vs. Perimeter

Hi, Todd.

"Circumference" is just a special term for the perimeter when applied
to circles.

We have to have a general term that applies to all shapes, or it would
get very confusing; there is no reason not to allow the word
"perimeter" to be applied to circles, as part of a discussion that
includes both circles and other shapes. For example, in the
"isoperimetric problem" we are looking for the figure with the
greatest area among all shapes with a given perimeter, and the answer
turns out to be the circle. We'd be in bad shape if we weren't allowed
to call that a perimeter, so that the circle was disqualified!

A dictionary that applies "perimeter" only to "edges" will we hope
define "edge" in a way that is not limited to straight lines. I'm
sure that's what was intended, since they just said "closed figure,"
not "polygon." In that sense, a circle has one edge.

See Eric Weisstein's World of Mathematics:

Perimeter
http://mathworld.wolfram.com/Perimeter.html

which defines perimeter as the total arc length of a boundary, and
specifically states that the perimeter of a circle is called the
circumference. Your math dictionary is probably aimed at a less
sophisticated audience, at least in that particular definition, which
does not impress me much.

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

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

```
Date: 05/09/2003 at 12:43:53
From: Todd
Subject: Thank you (Circumference vs. Perimeter)

Thanks for the prompt response. I appreciate the reasoning behind your
answer - makes sense to me! Kudos.
```
Associated Topics:
Elementary Definitions
Elementary Two-Dimensional Geometry
High School Definitions
High School Euclidean/Plane Geometry
Middle School Definitions
Middle School Two-Dimensional Geometry

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