Method of Exhaustion

The Method of Exhaustion is a technique used by mathematicians to find the area of complex shapes by approximating them with simpler shapes, like rectangles or triangles. They start with a rough shape that covers the area and then make it finer and closer to the actual shape by adding more, smaller shapes. With each step, the total area of these shapes gets closer to the true area. Over time, the approximation becomes so precise that they can confidently determine the exact area. This method laid the groundwork for integral calculus.