Approximations of pi

Approximations for the mathematical constant pi (π) in the history of mathematics reached an accuracy within 0.04% of the true value before the beginning of the Common Era (Archimedes). In Chinese mathematics, this was improved to approximations correct to what corresponds to about seven decimal digits by the 5th century.

Further progress was not made until the 15th century (Jamshīd al-Kāshī). Early modern mathematicians reached an accuracy of 35 digits by the beginning of the 17th century (Ludolph van Ceulen), and 126 digits by the 19th century (Jurij Vega), surpassing the accuracy required for any conceivable application outside of pure mathematics.

The record of manual approximation of π is held by William Shanks, who calculated 527 digits correctly in the years preceding 1873. Since the middle of the 20th century, the approximation of π has been the task of electronic digital computers; as of November 2016^[update], the record is 22.4 trillion digits.

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. After this, no further progress was made until the late medieval period.

Some Egyptologists have claimed that the ancient Egyptians used an approximation of π as  ²²⁄₇ from as early as the Old Kingdom. This claim has met with skepticism.

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