Approximations of π

Early history

The Chinese mathematicianLiu Hui in 263 CE computed π to between 3.141024 and 3.142708 by inscribing a 96-gon and 192-gon; the average of these two values is 3.141866 (accuracy 9·10). He also suggested that 3.14 was a good enough approximation for practical purposes. He has also frequently been credited with a later and more accurate result, π ≈ 3927⁄1250 = 3.1416 (accuracy 2·10), although some scholars instead believe that this is due to the later (5th-century) Chinese mathematician Zu Chongzhi. Zu Chongzhi is known to have computed π to be between 3.1415926 and 3.1415927, which was correct to seven decimal places. He also gave two other approximations of π: π ≈ 22⁄7 and π ≈ 355⁄113, which are not as accurate as his decimal result. The latter fraction is the best possible rational approximation of π using fewer than five decimal digits in the numerator and denominator. Zu Chongzhi's results surpass the accuracy reached in Hellenistic mathematics, and would remain without improvement for close to a millennium.