Using a technique equivalent to Richardson extrapolation, Huygens was able to shorten the inequalities used in Archimedes's method; in this case, by using the centre of the gravity of a segment of a parabola, he was able to approximate the centre of gravity of a segment of a circle, resulting in a faster and accurate approximation of the circle quadrature. From these theorems, Huygens obtained two set of values for : the first between 3.1415926 and 3.1415927, and the second between 3.1415926533 and 3.1415926538.
Using a technique equivalent to Richardson extrapolation, Huygens was able to shorten the inequalities used in Archimedes's method; in this case, by using the centre of the gravity of a segment of a parabola, he was able to approximate the centre of gravity of a segment of a circle, resulting in a faster and accurate approximation of the circle quadrature. From these theorems, Huygens obtained two set of values for : the first between 3.1415926 and 3.1415927, and the second between 3.1415926533 and 3.1415926538.