# Person: Chongzhi, Zu

Zu Chongzhi was a Chinese mathematician and astronomer. He introduced the approximation $\frac{355}{113}$ to $\pi$ which is correct to 6 decimal places.

### Mathematical Profile (Excerpt):

• Zu learnt other skills too for he excelled in engineering and was skilled in literary composition writing ten novels.
• During this time Zu worked on mathematics and astronomy.
• Zu, however, had an opponent at the court as far as his calendar was concerned.
• Despite having such a powerful opponent as Tai Faxin, Zu won approval for his calendar from Emperor Xiao-wu and the Tam-ing calendar was due to come into use in 464.
• Zu left the imperial service on the death of Emperor Xiao-wu and devoted himself entirely to his scientific studies.
• Having accurate knowledge of the lengths of the year and the month were necessary, but it is still not clear how Zu translated this into a cycle of 391 years.
• But Zu would know how to reduce fractions to their lowest terms by dividing top and bottom by the greatest common divisor.
• Before we leave our discussion of Zu's astronomical work we give further details of his work in this area.
• Zu's calculations of the length of the year were well within the range that allowed him to differentiate between the tropical and sidereal year.
• Jupiter takes about 12 years to complete its orbit but Zu was able to give a much more accurate value than that.
• Sadly Zu Chongzhi's book is lost.
• To compute this accuracy for π, Zu must have used an inscribed regular 24,576-gon and undertaken the extremely lengthy calculations, involving hundereds of square roots, all to 9 decimal place accuracy.
• However, given that Zu's work was considered very difficult and advanced, it is doubtful that it was found by a lucky numerical accident.
• In the latter part of his life Zu Chongzhi collaborated with his son, Zu Geng (or Zu Xuan), who was also an outstanding mathematician.

Born 429, Jiankang, (now Nanjing, Kiangsu province), China. Died 501, China.

View full biography at MacTutor

Ancient Chinese, Astronomy, Chinese, Origin China, Number Theory, Special Numbers And Numerals

Thank you to the contributors under CC BY-SA 4.0!

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non-Github:
@J-J-O'Connor
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### References

#### Adapted from other CC BY-SA 4.0 Sources:

1. O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive