Pi is an irrational number that has been approximated by several ratios. Here’s an history of the approximations of Pi as a ratio.
157/50 and 3927/1250
These two approximations, with values respectively 3.14 and 3.1416, were obtained by the Chinese mathematician Liu Hui in the 3rd century CE1.
355/113
The value of this ratio is 3.1415929. It is known since the 5th century CE, when it was computed by Zu Chongzhi (429 – 500). Zu was born in a family of calendar experts. When working on improving the calendar system, he felt necessary to get a better approximation of the constants used in his computations. The ratio 355/113 is however not as precise as his approximations of Pi standing between 3.1415926 and 3.1415927.
To be continued…
Sources of illustrations
Statue of Zu Chongzhi https://commons.wikimedia.org/wiki/File:%E7%A5%96%E5%86%B2%E4%B9%8B%E9%93%9C%E5%83%8F.jpg)
References
- Circle Measurements in Ancient China, Historia Mathematica, Volume 13, Issue 4, November 1986, Pages 325-340, https://www.sciencedirect.com/science/article/pii/0315086086900558 ↩︎
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