successions between various claimed ancestors of the Han and Xin houses. As the imperial librarian, Liu was able to set the definitive text of these ancient texts, and expunge earlier versions. The Doubting Antiquity School drew evidence from discrepancies between the texts edited by Liu and earlier or contemporaneous texts. For example, figures or events appearing in Liu's edited versions did not appear in earlier or contemporaneous texts. In some cases, Liu's text referred to a supposed earlier source that was not mentioned in any other texts. Although Liu has been vindicated in respect of some of these issues by later archaeological discoveries of older manuscripts that corroborated Liu's version, some other criticisms have become largely accepted by historians. Calculation of pi () For centuries before the reign of rebel Wang Mang (r. 9–23) the Chinese had used the value of 3 for their calculation of pi, 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 the improved approximation π ≈ 3.1547, 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 British biochemist, historian, and sinologist 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 Ancient Chinese mathematicians such as Zhang Heng (78–139) and Liu Hui (fl. 3rd century) would improve Liu's calculation for pi. Death 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. Astronomy A crater on Mars was named in his honor. See also Science and technology of the Han Dynasty Notes References Bielenstein,