Difference between revisions of "Circumference"
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'''Circumference''' is essentially a synonym for [[perimeter]]: for a given [[closed curve]] in the [[plane]], it is the distance one travels in a complete circuit of the curve. The term circumference is most frequently used to refer to the distance around a [[circle]], though it may refer to the distance around any [[smooth]] curve, while the term perimeter is typically reserved for [[polygon]]s. | '''Circumference''' is essentially a synonym for [[perimeter]]: for a given [[closed curve]] in the [[plane]], it is the distance one travels in a complete circuit of the curve. The term circumference is most frequently used to refer to the distance around a [[circle]], though it may refer to the distance around any [[smooth]] curve, while the term perimeter is typically reserved for [[polygon]]s. | ||
| − | In a circle of [[radius]] <math>r</math> and [[diameter]] <math>d = 2r</math>, the circumference <math>C</math> is given by < | + | ==Formulas== |
| + | In a circle of [[radius]] <math>r</math> and [[diameter]] <math>d = 2r</math>, the circumference <math>C</math> is given by | ||
| + | <cmath>C = \pi \cdot d = 2\pi \cdot r</cmath> Indeed, the [[constant]] <math>\pi</math> ([[pi]]) was originally defined to be the [[ratio]] of the circumference of a circle to the length of its diameter. | ||
| − | + | ==See Also== | |
| − | |||
| − | ==See | ||
Revision as of 13:56, 11 October 2015
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Circumference is essentially a synonym for perimeter: for a given closed curve in the plane, it is the distance one travels in a complete circuit of the curve. The term circumference is most frequently used to refer to the distance around a circle, though it may refer to the distance around any smooth curve, while the term perimeter is typically reserved for polygons.
Formulas
In a circle of radius 
and diameter 
, the circumference 
is given by
![\[C = \pi \cdot d = 2\pi \cdot r\]](http://latex.artofproblemsolving.com/3/5/8/358134d6a09f1e059e89656f96ac8faf3bb4d11a.png)
Indeed, the constant 
(pi) was originally defined to be the ratio of the circumference of a circle to the length of its diameter.
