Liu Hui established a solid algorithm for calculation of π to any accuracy.
- Zu Chongzhi was familiar with Liu Hui's work, and obtained greater accuracy by applying his algorithm to a 12288-gon.
- From Liu Hui's formula for 2N-gon:
- For 12288-gon inscribed in a unit radius circle:
- From Liu Hui's π inequality:
- In which
Truncated to eight significant digits:
That was the famous Zu Chongzhi π inequality.
Zu Chongzhi then used the interpolation formula by He Chengtian (何承天, 370-447) and obtained an approximating fraction: .
- Yuan dynasty mathematician Zhao Yu Xin worked on a variation of Liu Hui's π algorithm, by bisecting an inscribed square instead of a hexagon.
Read more about this topic: Liu Hui's π Algorithm
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