III.

Circumference and Area

The circumference—distance around the edge—of a circle is equal to a constant, pi (symbol p), times the circle’s diameter: C = pd. Since the diameter of a circle is equal to twice the circle’s radius, the circumference also equals two times pi times the radius: C = 2pr. Pi is one of the most important mathematical constants, and plays a role in many calculations and proofs in mathematics, physics, engineering, and other sciences. The first ten digits of pi are 3.141592654, although the approximations 3.14 or 3‡ are sufficiently accurate for many calculations.

Of all two-dimensional figures having the same perimeter, the circle has the greatest area. The area of a circle is equal to pi multiplied by the square of the circle’s radius: A = pr².