Liu Hui  

劉徽  
Born  c. 225^{[1]} 
Died  c. 295^{[1]} 
Occupation(s)  Mathematician, writer 
Liu Hui  

Traditional Chinese  劉徽  

Liu Hui (fl. 3rd century CE) was a Chinese mathematician who published a commentary in 263 CE on Jiu Zhang Suan Shu (The Nine Chapters on the Mathematical Art).^{[2]} He was a descendant of the Marquis of Zixiang of the Eastern Han dynasty and lived in the state of Cao Wei during the Three Kingdoms period (220–280 CE) of China.^{[3]}
His major contributions as recorded in his commentary on The Nine Chapters on the Mathematical Art include a proof of the Pythagorean theorem, theorems in solid geometry, an improvement on Archimedes's approximation of π, and a systematic method of solving linear equations in several unknowns. In his other work, Haidao Suanjing (The Sea Island Mathematical Manual), he wrote about geometrical problems and their application to surveying. He probably visited Luoyang, where he measured the sun's shadow.^{[3]}
Liu Hui expressed mathematical results in the form of decimal fractions that utilized metrological units (i.e., related units of length with base 10 such as 1 chǐ = 10 cùn, 1 cùn = 10 fēn, 1 fēn = 10 lí, etc.); this led Liu Hui to express a diameter of 1.355 feet as 1 chǐ, 3 cùn, 5 fēn, 5 lí.^{[4]} Han Yen (fl. 780804 CE) is thought to be the first mathematician that dropped the terms referring to the units of length and used a notation system akin to the modern decimal system and Yang Hui (c. 1238–1298 CE) is considered to have introduced a unified decimal system.^{[5]}
Liu provided a proof of a theorem identical to the Pythagorean theorem.^{[3]} Liu called the figure of the drawn diagram for the theorem the "diagram giving the relations between the hypotenuse and the sum and difference of the other two sides whereby one can find the unknown from the known."^{[6]}
In the field of plane areas and solid figures, Liu Hui was one of the greatest contributors to empirical solid geometry. For example, he found that a wedge with rectangular base and both sides sloping could be broken down into a pyramid and a tetrahedral wedge.^{[7]} He also found that a wedge with trapezoid base and both sides sloping could be made to give two tetrahedral wedges separated by a pyramid.^{[7]} He computed the volume of solid figures such as cone, cylinder, frustum of a cone, prism, pyramid, tetrahedron, and a wedge.^{[2]} However, he failed to compute the volume of a sphere and noted that he left it to a future mathematician to compute.^{[2]}
In his commentaries on The Nine Chapters on the Mathematical Art, he presented:
Liu Hui also presented, in a separate appendix of 263 AD called Haidao Suanjing or The Sea Island Mathematical Manual, several problems related to surveying. This book contained many practical problems of geometry, including the measurement of the heights of Chinese pagoda towers.^{[13]} This smaller work outlined instructions on how to measure distances and heights with "tall surveyor's poles and horizontal bars fixed at right angles to them".^{[14]} With this, the following cases are considered in his work:
Liu Hui's information about surveying was known to his contemporaries as well. The cartographer and state minister Pei Xiu (224–271) outlined the advancements of cartography, surveying, and mathematics up until his time. This included the first use of a rectangular grid and graduated scale for accurate measurement of distances on representative terrain maps.^{[15]} Liu Hui provided commentary on the Nine Chapter's problems involving building canal and river dykes, giving results for total amount of materials used, the amount of labor needed, the amount of time needed for construction, etc.^{[16]}
Although translated into English long beforehand, Liu's work was translated into French by Guo Shuchun, a professor from the Chinese Academy of Sciences, who began in 1985 and took twenty years to complete his translation.