The circumference is the linear distance around any closed curve or circular object. Circumference is a type of perimeter, although the term “perimeter” is usually reserved for polygons, while “circumference” is used for continuously differentiable curves.

Regardless of their size, all circles have the same ratio of circumference to diameter. This ratio is one of the best known and most important constants in mathematics, \pi.

    \[\pi = \frac{C}{d}\]

This gives us an easy way to calculate the circumference of a circle if we know its radius (remembering that the diameter of a circle is two times the radius, i.e., d = 2r):

    \[C = \pi{d} = 2\pi{r}\]

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