What is Circumference?

Date: 06/25/2001 at 12:48:12
From: raman
Subject: What is circumference?

What is circumference? My friend told me it's somewhat like the 
measurement of the outside of a circle, but I don't understand that. 
Can you help?

Date: 06/25/2001 at 13:31:58
From: Doctor Ian
Subject: Re: What is circumference?

Hi Raman,

Imagine a square, like

  A       B
   +-----+
   |     |
   |     |
   +-----+
  D       C

The 'perimeter' of the square is the sum of the distances

  perimeter = AB + BC + CD + DA

That is, it is the length of the _path_ that you would have to take to 
move all the way around the square, returning to the place where you 
started. 

We can extend the definition to regular polygons with more sides, 
e.g., 

    A _____ B
     /     \
  F /       \ C         perimeter = AB + BC + CD + DE + EF + FA
    \       /
     \_____/
     E     D

(A 'regular' polygon is a polygon whose sides and angles are 
identical. So a square is a regular polygon, but a parallelogram is 
not.)

A circle is basically a regular polygon with an infinite number of 
sides. For a circle, 'circumference' and 'perimeter' mean the same 
thing.

The American Heritage Dictionary gives these definitions for 
circumference:

http://www.bartleby.com/61/55/C0365500.html   

1. The boundary line of a circle. 
2a. The boundary line of a figure, area, or object. 
2b. abbreviation c or circ. The length of such a boundary. 

The word is originally from Latin circumferentia, from circumferns, 
circumferent-, present participle of circumferre, meaning "to carry 
around."

Does this help?  Write back if you'd like to talk about this some 
more, or if you have any other questions. 

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