Ancient China and Pi

In 264 CE, the Chinese mathematician Liu Hui used a method to determine the value of pi similar to that used by Archimedes.

Using a polygon with 192 sides, Liu Hui determined that 3.141024 < pi < 3.142704. Using a much more faceted polygon, with 3,072 sides, he found that pi = 3.14159. This extremely accurate calculation was actually improved upon by a father and son expert in mathematics and astronomy, Tsu Ch’ung-Chih and Tsu Ken-Chih. Although the details of their calculations do not survive, the result they achieved was an approximation of pi = 355/113, approximately 3.1415929… This value is less than 10-millionths of 1 percent from the value calculated today. Using the polygon method, they would have required a polygon of more than 24 thousand sides, with hundreds of square root calculations carried out to an accuracy of approximately 9 decimal places.

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