Archimedes' proof

Archimedes' proof demonstrates that the area of a circle is equal to the area of a triangle with a base equal to the circle's diameter and a height equal to the circle's radius. He approached this by inscribing numerous polygons within the circle and calculating their areas, showing that as the number of sides increases, the polygon's area approaches that of the circle. By carefully comparing these areas, he concluded that the area of the circle can be expressed as π (pi) times the square of its radius, establishing a foundational principle in geometry.