First, some background information:
1. A
unit circles is a circle with a radius equal to 1.
2. The
circumference of a circle is equal to 2πr, and the area = πr2
3. Since
in a unit circle r=1, the circumference is equal to 2*π and
the area is equal to π
We can also know that a circle can be described on a coordinate
plane as x2+y2=1 (see http://www.mathwarehouse.com/geometry/circle/equation-of-a-circle.php), so
y=
, and
the area under this curve would be the area of half of a unit circle (the area
of a unit circle is equal to π, so the area of half a circle is equal to 
).
As you can see from the diagram below, the area under the curve
is 
=
.
Therefore π = 2* .
Since π = 2* ,
another way of writing 2*π (the circumference of a circle) is as
follows: 2*2*