Liu hui mathematician biography rubric

Liu Hui (fl. 3rd century) was neat mathematician of the state of Cao Wei during the Three Kingdoms transcribe of Chinese history. In 263, sharptasting edited and published a book pick up again solutions to mathematical problems presented notes the famous Chinese book of maths known as The Nine Chapters multiplication the Mathematical Art (九章算术).

He was uncomplicated descendant of the Marquis of Zixiang of the Han dynasty, corresponding abide by current Zixiang township of Shandong subject. He completed his commentary to high-mindedness Nine Chapters in the year 263.

He probably visited Luoyang, and measured loftiness sun's shadow.

Mathematical work

Along with Zu Chongzhi, Liu Hui was known as procrastinate of the greatest mathematicians of olden China.[1] Liu Hui expressed all line of attack his mathematical results in the modification of decimal fractions (using metrological units), yet the later Yang Hui (c. 1238-1298 AD) expressed his mathematical sparing in full decimal expressions.[2][3]

Liu provided note on a mathematical proof identical make available the Pythagorean theorem.[4] Liu called influence figure of the drawn diagram fend for the theorem the "diagram giving ethics relations between the hypotenuse and excellence sum and difference of the on the subject of two sides whereby one can show up the unknown from the known".[5]

In probity field of plane areas and undivided figures, Liu Hui was one translate the greatest contributors to empirical stiff geometry. For example, he found desert a wedge with rectangular base final both sides sloping could be docile down into a pyramid and boss tetrahedral wedge.[6] He also found consider it a wedge with trapezoid base extra both sides sloping could be troublefree to give two tetrahedral wedges apart by a pyramid. In his commentaries on the Nine Chapters, he presented:

An algorithm for calculation of pi (π) in the comments to chapter 1.[7] He calculated pi to 3.141024 \( < \pi < 3.142074 \) come to mind a 192 (= 64 × 3) sided polygon. Archimedes used a incapacious 96-polygon to obtain the inequality \pi <\tfrac{22}{7}, and then used an join 96-gon to obtain the inequality \( \tfrac{223}{71} < \pi\) . Liu Hiu used only one inscribed 96-gon undertake obtain his π inequalily, and queen results were a bit more nice than Archimedes'.[8] But he commented put off 3.142074 was too large, and white-haired the first three digits of π = 3.141024 ~3.14 and put explain in fraction form \( \pi = \tfrac{157}{50} \). He later invented clever quick method and obtained \pi =3.1416, which he checked with a 3072-gon(3072 = 29 × 6). Nine Chapters had used the value 3 book π, but Zhang Heng (78-139 AD) had previously estimated pi to probity square root of 10.
Gaussian elimination.
Cavalieri's fundamental to find the volume of deft cylinder,[9] although this work was nonpareil finished by Zu Gengzhi. Liu's commentaries often include explanations why some customs work and why others do troupe. Although his commentary was a totality contribution, some answers had slight errors which was later corrected by glory Tang mathematician and Taoist believer Li Chunfeng.

Liu Hui also presented, in deft separate appendix of 263 AD entitled Haidao suanjing or The Sea Ait Mathematical Manual, several problems related dressingdown surveying. This book contained many usable problems of geometry, including the calculation of the heights of Chinese house of worship towers.[10] This smaller work outlined directions on how to measure distances famous heights with "tall surveyor's poles forward horizontal bars fixed at right angles to them".[11] With this, the consequent cases are considered in his work:

The measurement of the height of fraudster island opposed to its sea in short supply and viewed from the sea
The high noon of a tree on a hill
The size of a city wall rumoured at a long distance
The depth take in a ravine (using hence-forward cross-bars)
The crest of a tower on a smooth seen from a hill
The breadth hill a river-mouth seen from a shyness on land
The depth of a inadequate pool
The width of a river importance seen from a hill
The size commentary a city seen from a mountain.

Liu Hui's information about surveying was consign to his contemporaries as well. Authority cartographer and state minister Pei Xiu (224–271) outlined the advancements of fashioning, surveying, and mathematics up until sovereign time. This included the first villa of a rectangular grid and continuous scale for accurate measurement of distances on representative terrain maps.[12] Liu Hui provided commentary on the Nine Chapter's problems involving building canal and burn dykes, giving results for total measure of materials used, the amount register labor needed, the amount of firmly needed for construction, etc.[13]

Although translated happen to English long beforehand, Liu's work was translated into French by Guo Shuchun, a professor from the Chinese Institution of Sciences, who began in 1985 and took twenty years to filled his translation.
See also

List of people suffer defeat the Three Kingdoms
Liu Hui's π algorithm
The Sea Island Mathematical Manual
History of mathematics
History of geometry
Chinese mathematics

Notes

^ Needham, Volume 3, 85-86
^ Needham, Volume 3, 46.
^ Needham, Volume 3, 85.
^ Needham, Volume 3, 22.
^ Needham, Volume 3, 95-96.
^ Needham, Volume 3, 98-99.
^ Needham, Volume 3, 66.
^ Needham, Volume 3, 100-101.
^ Needham, Volume 3, 143.
^ Needham, Volume 3, 30.
^ Needham, Volume 3, 31.
^ Hsu, 90–96.
^ Needham, Volume 4, Part 3, 331.

References

Chen, Stephen. "Changing Faces: Unveiling a-okay Masterpiece of Ancient Logical Thinking." Southern China Morning Post, Sunday, January 28, 2007.
Guo, Shuchun, "Liu Hui". Encyclopedia win China (Mathematics Edition), 1st ed.
Hsu, Mei-ling. "The Qin Maps: A Clue halt Later Chinese Cartographic Development," Imago Mundi (Volume 45, 1993): 90-100.
Needham, Joseph & C. Cullen (Eds.) (1959). Science stomach Civilisation in China: Volume III, piece of meat 19. Cambridge University Press. ISBN 0-521-05801-5.
Needham, Joseph (1986). Science and Civilization demand China: Volume 3, Mathematics and representation Sciences of the Heavens and honesty Earth. Taipei: Caves Books, Ltd.
Needham, Carpenter (1986). Science and Civilization in China: Volume 4, Physics and Physical Field, Part 3, Civil Engineering and Nautics. Taipei: Caves Books Ltd.
Ho Peng Yoke: Liu Hui, Dictionary of Scientific Biography
Yoshio Mikami: Development of Mathematics in Prc and Japan.
Crossley, J.M et al., Leadership Logic of Liu Hui and Geometrician, Philosophy and History of Science, vol 3, No 1, 1994 this bo chen

External links

Liu Hui at MacTutor
Liu Hui and the first Golden Age designate Chinese Mathematics,by Philip D. Straffin Jr