Liu Xin

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For the emperor named Liu Xin, see Emperor Ai of Han.
For other uses, see Liu Xin (disambiguation).
This is a Chinese name; the family name is Liu.
Liu Xin
Traditional Chinese 劉歆
Simplified Chinese 刘歆

Liu Xin (Chinese: 劉歆; c. 50 BC – AD 23),[1] courtesy name Zijun (Chinese: 子駿), was a Chinese astronomer, historian, and editor during the Western Han Dynasty (206 BC-AD 9) and Xin Dynasty (AD 9–23). He later changed his name to Liu Xiu (Chinese: 劉秀) due to the naming taboo of Emperor Ai of Han. He was the son of Confucian scholar Liu Xiang (77–6 BC) and an associate of other prominent thinkers such as the philosopher Huan Tan (d. 28 AD).[2] Liu founded the Old Text school of Confucianism.


As a curator of the imperial library he was the first to establish a library classification system and the first book notation system. At this time the library catalog was written on scrolls of fine silk and stored in silk bags.[3]

Calculation of pi (π)[edit]

For centuries before the reign of Wang Mang (r. 9–23) the Chinese had used the value of 3 for their calculation of pi,[4] the ratio of a circle's circumference to its diameter (now known to be approximately equal to 3.14159). Between the years 1 and 5, while working for the de facto head of state Wang Mang, Liu Xin was the first to give a geometrical figure which implies a more accurate value of pi at 3.1457,[5] although the exact method he used to reach this figure is unknown.[6] However, the ancient record of Liu Xin's 'Jia Liang Hu' 嘉量斛 standard is still preserved in Beijing, which Joseph Needham quotes below with modern references for archaic units (Wade-Giles spelling):[6]

The standardised chia liang hu (has) a square with each side 1 chhih (foot) long, and outside it a circle. The distance from each corner of the square to the circle (thiao phang) is 9 li 5 hao. The area of the circle (mu) is 162 (square) tshun (inches), the depth 1 chhih (foot), and the volume (of the whole) 1620 (cubic) tshun (inches).[6]

Later mathematicians such as Zhang Heng (78–139) and Liu Hui (fl. 3rd century) would improve Liu's calculation for pi.[7]


Although Liu Xin was originally a loyal partisan of Wang Mang, after Wang's troops suffered defeat on July 7, 23 at the Battle of Kunyang, Liu Xin plotted with others to overthrow Wang Mang. The plot was discovered, and all the conspirators committed suicide or were executed.[8]


A crater on Mars was named in his honor.

See also[edit]


  1. ^ Cullen, Christopher (2007) Astronomy and Mathematics in Ancient China: The 'Zhou Bi Suan Jing' Cambridge, UK: Cambridge University Press
  2. ^ Crespigny, 338.
  3. ^ Hur-Li Lee, "Epistemic foundation of bibliographic classification in early China: A Ru classicist perspective," Journal of Documentation (2012) 68#3 pp 378-401. pool will shiftonline
  4. ^ Needham, Volume 3, 99.
  5. ^ 中西數學史的比較 (1991), 44-47
  6. ^ a b c Needham, Volume 3, 100.
  7. ^ Needham, Volume 3, 100–101.
  8. ^ Bielenstein, 247–248


  • Bielenstein, Hans. (1986). "Wang Mang, the Restoration of the Han Dynasty, and Later Han", in The Cambridge History of China: Volume I: the Ch'in and Han Empires, 221 B.C. – A.D. 220. Edited by Denis Twitchett and Michael Loewe. Cambridge: Cambridge University Press. ISBN 0-521-24327-0.
  • Bin, Hansheng, "Liu Xin". Encyclopedia of China (Philosophy Edition), 1st ed.
  • Crespigny, Rafe de. (2007). A Biographical Dictionary of Later Han to the Three Kingdoms (23-220 AD). Leiden: Koninklijke Brill. ISBN 90-04-15605-4.
  • Needham, Joseph (1986). Science and Civilization in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth. Taipei: Caves Books, Ltd.

External links[edit]