For centuries the Chinese approximated pi as 3; Liu Xin (d. CE 23) made the first known Chinese attempt at a more accurate calculation of 3.154, but there is no record detailing the method he used to obtain this figure.Needham (1986), Volume 3, 99–100. In his work around 130,Needham (1986), Volume 3, 100. Zhang Heng compared the celestial circle to the diameter of the earth, proportioning the former as 736 and the latter as 232, thus calculating pi as 3.1724.Berggren, Borwein & Borwein (2004), 27. In Zhang's day, the ratio 4:3 was given for the area of a square to the area of its inscribed circle and the volume of a cube and volume of the inscribed sphere should also be 42:32. In formula, with D as diameter and V as volume, D3:V = 16:9 or V=D3; Zhang realized that the value for diameter in this formula was inaccurate, noting the discrepancy as the value taken for the ratio.Arndt and Haenel (2001), 176. Zhang then attempted to remedy this by amending the formula with an additional D3, hence V=D3 + D3 = D3. With the ratio of the volume of the cube to the inscribed sphere at 8:5, the implied ratio of the area of the square to the circle is √8:√5.Arndt and Haenel (2001), 177. From this formula, Zhang calculated pi as the square root of 10 (or approximately 3.162).Yan (2007), 128.Wilson (2001), 16. In the 3rd century, Liu Hui made the calculation more accurate with his π algorithm, which allowed him to obtain the value 3.14159.Needham (1986), Volume 3, 100–101. Later, Zu Chongzhi (429–500) approximated pi as or 3.141592, the most accurate calculation for pi the ancient Chinese would achieve.Berggren, Borwein & Borwein (2004), 20 & 24–26.
For centuries the Chinese approximated pi as 3; Liu Xin (d CE 23) made the first known Chinese attempt at a more accurate calculation of 3154 but there is no record detailing the method he used to obtain this figureNeedham (1986) Volume 3 99–100 In his work around 130Needham (1986) Volume 3 100 Zhang Heng compared the celestial circle to the diameter of the earth proportioning the former as 736 and the latter as 232 thus calculating pi as 31724Berggren Borwein & Borwein (2004) 27 In Zhang's day the ratio 43 was given for the area of a square to the area of its inscribed circle and the volume of a cube and volume of the inscribed sphere should also be 4232 In formula with D as diameter and V as volume D3V = 169 or V=D3; Zhang realized that the value for diameter in this formula was inaccurate noting the discrepancy as the value taken for the ratioArndt and Haenel (2001) 176 Zhang then attempted to remedy this by amending the formula with an additional D3 hence V=D3 + D3 = D3 With the ratio of the volume of the cube to the inscribed sphere at 85 the implied ratio of the area of the square to the circle is √8√5Arndt and Haenel (2001) 177 From this formula Zhang calculated pi as the square root of 10 (or approximately 3162)Yan (2007) 128Wilson (2001) 16 In the 3rd century Liu Hui made the calculation more accurate with his π algorithm which allowed him to obtain the value 314159Needham (1986) Volume 3 100–101 Later Zu Chongzhi (429–500) approximated pi as or 3141592 the most accurate calculation for pi the ancient Chinese would achieveBerggren Borwein & Borwein (2004) 20 & 24–26