Why is the formula of circle 2pie r?

Answer 1

π was originally known (to the Greeks, I think) as the ratio of the circumference of a circle to its diameter, thus:

circumference/diameter = π

which with rearranging becomes:

circumference = π x diameter

However, the diameter of the circle is the distance from one point on its circumference to its centre and then onto another point on the circumference so it is also twice the radius in length, that is:

diameter = 2 x radius

which can be substituted back into the formula above to yield:

circumference = π x 2 x radius

or

circumference = 2 x π x radius

which is usually abbreviated, in algebra, to:

circumference = 2πr

with r representing the radius of the circle, and π the ratio as previously described.