Liu Xin (Chinese: 劉歆; Wade–Giles: Liu Hsin) (ca. 50 BC – AD 23), later changed name to Liu Xiu (Chinese: 劉秀; pinyin: Liú Xiù), courtesy name Zijun (Chinese: 子駿; pinyin: Zǐjùn), was a Chinese astronomer, historian, and editor during the Xin Dynasty (AD 9–23). 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). Liu founded the Old Text School of Confucianism. Liu created a new astronomical system, called "Triple Concordance". He published this system in the year 8 as section of his textbook. In it he provided the following periods:
- The Moon phase period (synodic month): 29 43/81 days.
- A total of 235 synodic months add up to 19 years.
Therefore his number of days in one year was 365.25016, which is 11 minutes longer than the current value.
Liu created a catalog of 1080 stars, where he used the scale of 6 magnitudes. He also calculated periods for planets.
For centuries before the reign of Wang Mang (r. 9–23) the Chinese had used the value of 3 for their calculation of pi. 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 more accurate calculation of pi at 3.1457, although the exact method he used to reach this figure is unknown. However, the ancient record of Liu Xin's 'Jia Liang Hu' standard is still preserved in Beijing, which Joseph Needham quotes below with modern references for archaic units (Wade-Giles spelling):
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).
Later mathematicians such as Zhang Heng (78–139) and Liu Hui (fl. 3rd century) would improve Liu's calculation for pi approximate to the standard of pi used in modern times.
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.
A crater on Mars was named in his honor.