In Measurement of a Circle, he did this by drawing a larger regular hexagon outside a circle then a smaller regular hexagon inside the circle, and progressively doubling the number of sides of each regular polygon, calculating the length of a side of each polygon at each step. As the number of sides increases, it becomes a more accurate approximation of a circle. After four such steps, when the polygons had 96 sides each, he was able to determine that the value of lay between 3 (approx. 3.1429) and 3 (approx. 3.1408), consistent with its actual value of approximately 3.1416. He also proved that the area of a circle was equal to multiplied by the square of the radius of the circle ().
In Measurement of a Circle he did this by drawing a larger regular hexagon outside a circle then a smaller regular hexagon inside the circle and progressively doubling the number of sides of each regular polygon calculating the length of a side of each polygon at each step As the number of sides increases it becomes a more accurate approximation of a circle After four such steps when the polygons had 96 sides each he was able to determine that the value of lay between 3 (approx 31429) and 3 (approx 31408) consistent with its actual value of approximately 31416 He also proved that the area of a circle was equal to multiplied by the square of the radius of the circle ()