#
The Area of a Circle

Why is the area of a circle pi times the square of the radius?
The
usual definition of pi is the ratio of the circumference of a
circle to
its diameter, so that the circumference of a circle is pi times
the
diameter, or 2 pi times the radius. The animation above shows that
a
circle can be cut and rearranged to closely resemble a
parallelogram
(with height r and base pi times r) of area pi times the square of
the
radius. By dividing the circle into more than eight slices, the
approximation obtained in this manner would be even better. By
dividing
the circle into more and more slices, the approximating
parallelograms
approximate the area of the circle arbitrarily close. This give a
geometric justification that the area of a circle really is "pi r
squared".

For another justification for the area of a circle, see The Area of a Circle II.

### Other Animated Sites

The Area of a Circle
II
The Pythagorean Theorem

The Sine Curve

The Cosine Curve

WKU
Mathematics Department .|. WKU
Online

*Last updated, Jan. 29, 2008*

Tom.Richmond@wku.edu