How did Liu Hui improve the approximation of pi?

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East Asian mathematics Counting boards and markers, or counting rods, were used in China to solve systems of linear equations. This is an example from the 1st century ce.

In the 3rd century CE, the Chinese mathematician Liu Hui significantly improved the approximation of pi by refining polygonal methods. While earlier texts like The Nine Chapters on the Mathematical Art utilized a simplified value of 3, Liu Hui employed a more rigorous approach by dissecting regions into infinitely many pieces to prove the correctness of geometric algorithms.123

Through his work, Liu Hui calculated a value for pi of approximately 3.14159. His commentary on The Nine Chapters also introduced two specific approximations: a lower bound of 157/50 (3.14) and a higher bound of 3,927/1,250 (3.1416). By focusing on the geometric dissection of circles, he moved beyond mere estimation to establish a more precise mathematical foundation for calculating the area of a circle.132