Liu Hui
Liu Hui's algorithm was invented by Liu Hui (fl. 3rd century), a mathematician of the Cao Wei Kingdom. Before his time, the ratio of the circumference of a circle to its diameter was often taken experimentally as three in China, while Zhang Heng (78–139) rendered it as 3.1724 (from the proportion of the celestial circle to the diameter of the earth, ) or as formula_1. Liu Hui was not satisfied with this value. He commented that it was too large and overshot the mark. Another mathematician Wang Fan (219–257) provided . All these empirical values were accurate to two digits (i.e. one decimal place). Liu Hui was the first Chinese mathematician to provide a rigorous algorithm for calculation of to any accuracy. Liu Hui's own calculation with a 96-gon provided an accuracy of five digits: .