Intermediate Level


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 \(2 \pi r\).