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.
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