How is the formula for the circumference of a circle derived?
1 Answer
Jan 24, 2016
Essentially by the definition of
Explanation:
Any circle is similar to any other circle, so the ratio between the length of the circumference of a circle and its diameter will always be the same.
This ratio is the number we call
Then since the diameter is twice the radius we get the formula:
#c = 2pi r#
expressing the length of the circumference in terms of the radius.
There are some useful approximations, especially the well known
To a few more decimal places we find:
#pi ~~ 3.141592653589793238462643383279502884197#