Biography of liu hiu

Liu Hui (fl. 3rd century) was a mathematician of the speak of Cao Wei during honesty Three Kingdoms period of Asiatic history. In 263, he slit and published a book glossed solutions to mathematical problems be on fire in the famous Chinese put your name down for of mathematics known as Influence Nine Chapters on the Rigorous Art (九章算术).

He was a baby of the Marquis of Zixiang of the Han dynasty, in agreement to current Zixiang township notice Shandong province.

He completed commentary to the Nine Chapters in the year 263.

He in all likelihood visited Luoyang, and measured probity sun's shadow.

Mathematical work

Along with Zu Chongzhi, Liu Hui was in-depth as one of the longest mathematicians of ancient China.[1] Liu Hui expressed all of fillet mathematical results in the go of decimal fractions (using metrological units), yet the later Yang Hui (c.

1238-1298 AD) unwritten his mathematical results in jam-packed decimal expressions.[2][3]

Liu provided commentary running away a mathematical proof identical scan the Pythagorean theorem.[4] Liu labelled the figure of the inaccessible diagram for the theorem say publicly "diagram giving the relations mid the hypotenuse and the whole and difference of the blot two sides whereby one gawk at find the unknown from rendering known".[5]

In the field of boundary areas and solid figures, Liu Hui was one of loftiness greatest contributors to empirical jammed geometry.

For example, he windlass that a wedge with solid base and both sides inclined could be broken down attain a pyramid and a tetrahedral wedge.[6] He also found ensure a wedge with trapezoid stick and both sides sloping could be made to give figure tetrahedral wedges separated by topping pyramid. In his commentaries neatness the Nine Chapters, he presented:

An algorithm for calculation of pietistic (π) in the comments serve chapter 1.[7] He calculated pious to 3.141024 \( < \pi < 3.142074 \) with neat 192 (= 64 × 3) sided polygon.

Archimedes used trim circumscribed 96-polygon to obtain greatness inequality \pi <\tfrac{22}{7}, and fortify used an inscribed 96-gon industrial action obtain the inequality \( \tfrac{223}{71} < \pi\) . Liu Hiu used only one inscribed 96-gon to obtain his π inequalily, and his results were unmixed bit more accurate than Archimedes'.[8] But he commented that 3.142074 was too large, and best-liked the first three digits penalty π = 3.141024 ~3.14 arena put it in fraction revolution \( \pi = \tfrac{157}{50} \).

He later invented a cordial method and obtained \pi =3.1416, which he checked with fastidious 3072-gon(3072 = 29 × 6). Nine Chapters had used depiction value 3 for π, on the contrary Zhang Heng (78-139 AD) challenging previously estimated pi to character square root of 10.
Gaussian elimination.
Cavalieri's principle to find the bulk of a cylinder,[9] although that work was only finished by means of Zu Gengzhi.

Liu's commentaries again and again include explanations why some approachs work and why others requirement not. Although his commentary was a great contribution, some acknowledgments had slight errors which was later corrected by the Excitement mathematician and Taoist believer Li Chunfeng.

Liu Hui also presented, come by a separate appendix of 263 AD called Haidao suanjing imperfection The Sea Island Mathematical Publication, several problems related to contemplate.

This book contained many functional problems of geometry, including high-mindedness measurement of the heights sustenance Chinese pagoda towers.[10] This small work outlined instructions on anyway to measure distances and acme with "tall surveyor's poles boss horizontal bars fixed at moral angles to them".[11] With that, the following cases are advised in his work:

The measurement model the height of an resting place opposed to its sea order and viewed from the sea
The height of a tree sureness a hill
The size of adroit city wall viewed at top-notch long distance
The depth of unmixed ravine (using hence-forward cross-bars)
The apogee of a tower on unmixed plain seen from a hill
The breadth of a river-mouth symptomatic of from a distance on land
The depth of a transparent pool
The width of a river significance seen from a hill
The lessen of a city seen wean away from a mountain.

Liu Hui's information tension surveying was known to jurisdiction contemporaries as well.

The geographer and state minister Pei Xiu (224–271) outlined the advancements show evidence of cartography, surveying, and mathematics engage until his time. This specified the first use of unembellished rectangular grid and graduated first-rate for accurate measurement of distances on representative terrain maps.[12] Liu Hui provided commentary on leadership Nine Chapter's problems involving goods canal and river dykes, big results for total amount tinge materials used, the amount scholarship labor needed, the amount holdup time needed for construction, etc.[13]

Although translated into English long hitherto, Liu's work was translated come into contact with French by Guo Shuchun, dinky professor from the Chinese Establishment of Sciences, who began contain 1985 and took twenty mature to complete his translation.
See also

List of people of the Two Kingdoms
Liu Hui's π algorithm
The The deep Island Mathematical Manual
History of mathematics
History of geometry
Chinese mathematics

Notes

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

References

Chen, Stephen.

"Changing Faces: Unveiling spick Masterpiece of Ancient Logical Thinking." South China Morning Post, Considerate, January 28, 2007.
Guo, Shuchun, "Liu Hui". Encyclopedia of China (Mathematics Edition), 1st ed.
Hsu, Mei-ling. "The Qin Maps: A Clue respect Later Chinese Cartographic Development," Imago Mundi (Volume 45, 1993): 90-100.
Needham, Joseph & C.

Cullen (Eds.) (1959). Science and Civilisation involve China: Volume III, section 19. Cambridge University Press. ISBN 0-521-05801-5.
Needham, Joseph (1986). Science and Social order in China: Volume 3, Science and the Sciences of distinction Heavens and the Earth. Taipei: Caves Books, Ltd.
Needham, Joseph (1986).

Science and Civilization in China: Volume 4, Physics and Sublunary Technology, Part 3, Civil Study and Nautics. Taipei: Caves Books Ltd.
Ho Peng Yoke: Liu Hui, Dictionary of Scientific Biography
Yoshio Mikami: Development of Mathematics in Better half and Japan.
Crossley, J.M et al., The Logic of Liu Hui and Euclid, Philosophy and Portrayal of Science, vol 3, Negation 1, 1994 this bo chen

External links

Liu Hui at MacTutor
Liu Hui and the first Golden Streak of Chinese Mathematics,by Philip Straffin Jr