# Approximations of π

**In March 2019 Emma Haruka Iwao, a Google employee from Japan, calculated to a new world record length of 31 trillion digits. The record was surpassed on January 29, 2020 by Timothy Mullican, who calculated to 50 trillion digits using retired enterprise server equipment and the software y-cruncher.**

### About Approximations of π in brief

In March 2019 Emma Haruka Iwao, a Google employee from Japan, calculated to a new world record length of 31 trillion digits with the help of the company’s cloud computing service. The record was surpassed on January 29, 2020 by Timothy Mullican, who calculated to 50 trillion digits using retired enterprise server equipment and the software y-cruncher. The best known approximations to π dating to before the Common Era were accurate to two decimal places; this was improved upon in Chinese mathematics in particular by the mid-first millennium, to an accuracy of seven decimal places. Babylonian mathematics usually approximated π to 3, sufficient for the architectural projects of the time. Some Egyptologists claim that the ancient Egyptians used an approximation of π as 22⁄7 = 3. 142857. In Gupta-era India, mathematician Aryabhata in his astronomical treatise Āryabhaṭīya calculated the value of ρ to five figures π using the circumference of a circle to 3.1416. His 15th-century commentator Nilakantha Nilakaji has argued that this is not an approximation, but that the value is incommensurable. In the 2nd century CE, Ptolemy used the value 377⁄120, the first known approximation accurate to three decimal places. The Chinese mathematician Liu Hui in 263 CE computed π.

to between 3. 15th century CE. Zu Chongzhi’s result surpasses the accuracy reached in Hellenistic mathematics, and would remain without improvement for close to a millennium. The latter fraction is the best possible rational approximation using fewer than five decimal digits in the numerator and denominator. It is now known as the π series for infinite series of digits, or π, as the number of digits in this series is known as π-1-2-3-4-5-6-7-8-9-10-11-12-13-14-15-16-17-18-19-20-21-22-23-24-25-26-28-29-30-31-32-34-33-36-34, and it is now the most accurate approximation for π in the history of mathematics. It has been known for nearly a millennium, until the 14th century, when Indian mathematician and astronomer Madhava Sangamhava discovered the infinite series for ρ, which is now about seven digits in length. The number of decimal places in π is known to be about five in the Chinese school of astronomy and mathematics, or about seven in the Indian mathematics school of Madhav Madhhava, founder of the Kerala school of mathematics and mathematics. The value of pi is about 528 percent below the exact value, but it is close to being within 0. 04% of the true value of the constant.

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