Intermediate Level

Areas

The application illustrates the determination of the area of a circle by its decomposition in an increasing number of circular sectors, recreating the process used by Archimedes (287-212 BC) to prove the relation $$P = 2A$$ between the perimeter of the unit circumference ($$P$$) and the area of the unit circle ($$A = \pi$$).

Since the number $$\pi$$ is, by definition, the constant ratio between the perimeter and the measure of the diameter of any circumference, the perimeter of a circumference of radius $$r$$ is equal to $$2 \pi r$$.