Pi Day CountDown #6 – Pi and Zu Chongzhi

Like Liu Hui, Zu Chongzhi is considered one of the greatest mathematicians of  ancient china. Also, like Liu Hui, Zu Chongzhi also manages to compute a highly accurate approximation of Pi.

Zi Chongzhi, a chinese mathematician and astronomer who lived in the 5th century AD
Zi Chongzhi, a chinese mathematician and astronomer who lived in the 5th century AD

Using the same technique as Liu Hui, Zi Chongzhi knows that he can approximate the area of a circle by calculating the area of a regular polygon with a large number of sides. The more sides he adds the better his approximation becomes.

Unlike Liu Hui, Zu Chongzhi calculates the area of a 24,576 sided regular polygon, which means that his approximation is much closer then Liu Hui, who only calculated the area of a regular polygon between 96 and 192 sides. In the end Zu Chongzhi manages to trap the value of \pi between two numbers:

3.141592 < \pi < 3.1415927

And from there he estimates that the value of \pi is approximately 355/113. Which is one of the most accurate approximation of \pi in the Ancient world.

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