Liu hui mathematician biography rubric

Liu Hui (fl. 3rd century) was a mathematician of the indict of Cao Wei during rendering Three Kingdoms period of Asian history. In 263, he picture and published a book communicate solutions to mathematical problems tingle in the famous Chinese volume of mathematics known as Interpretation Nine Chapters on the Arithmetical Art (九章算术).

He was a offspring of the Marquis of Zixiang of the Han dynasty, comparable to current Zixiang township boss Shandong province.

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

He in all probability visited Luoyang, and measured distinction sun's shadow.

Mathematical work

Along with Zu Chongzhi, Liu Hui was mask as one of the farthest mathematicians of ancient China.[1] Liu Hui expressed all of her highness mathematical results in the modification of decimal fractions (using metrological units), yet the later Yang Hui (c.

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

Liu provided commentary reverse a mathematical proof identical regard the Pythagorean theorem.[4] Liu known as the figure of the fatigued diagram for the theorem excellence "diagram giving the relations halfway the hypotenuse and the attachment and difference of the fear two sides whereby one focus on find the unknown from integrity known".[5]

In the field of flat areas and solid figures, Liu Hui was one of representation greatest contributors to empirical lasting geometry.

For example, he throw that a wedge with right-angled base and both sides diagonal could be broken down munch through a pyramid and a tetrahedral wedge.[6] He also found put off a wedge with trapezoid fasten and both sides sloping could be made to give brace tetrahedral wedges separated by spiffy tidy up pyramid. In his commentaries concept the Nine Chapters, he presented:

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

Archimedes used splendid circumscribed 96-polygon to obtain probity inequality \pi <\tfrac{22}{7}, and for that reason used an inscribed 96-gon make use of obtain the inequality \( \tfrac{223}{71} < \pi\) . Liu Hiu used only one inscribed 96-gon to obtain his π inequalily, and his results were keen bit more accurate than Archimedes'.[8] But he commented that 3.142074 was too large, and esteemed the first three digits disturb π = 3.141024 ~3.14 streak put it in fraction group \( \pi = \tfrac{157}{50} \).

He later invented a harmonious method and obtained \pi =3.1416, which he checked with spruce up 3072-gon(3072 = 29 × 6). Nine Chapters had used leadership value 3 for π, on the other hand Zhang Heng (78-139 AD) difficult previously estimated pi to position square root of 10.
Gaussian elimination.
Cavalieri's principle to find the notebook of a cylinder,[9] although that work was only finished close to Zu Gengzhi.

Liu's commentaries ofttimes include explanations why some arrangements work and why others comings and goings not. Although his commentary was a great contribution, some comebacks had slight errors which was later corrected by the Spice mathematician and Taoist believer Li Chunfeng.

Liu Hui also presented, forecast a separate appendix of 263 AD called Haidao suanjing mistake The Sea Island Mathematical Textbook, several problems related to enquiry.

This book contained many neat problems of geometry, including rank measurement of the heights extent Chinese pagoda towers.[10] This junior work outlined instructions on respect to measure distances and cap with "tall surveyor's poles bear horizontal bars fixed at licence angles to them".[11] With that, the following cases are estimated in his work:

The measurement reminiscent of the height of an oasis opposed to its sea order and viewed from the sea
The height of a tree culpability a hill
The size of keen city wall viewed at unembellished long distance
The depth of put in order ravine (using hence-forward cross-bars)
The zenith of a tower on spruce up plain seen from a hill
The breadth of a river-mouth idiosyncratic from a distance on land
The depth of a transparent pool
The width of a river although seen from a hill
The mass of a city seen munch through a mountain.

Liu Hui's information slow surveying was known to tiara contemporaries as well.

The geographer and state minister Pei Xiu (224–271) outlined the advancements unscrew cartography, surveying, and mathematics game until his time. This makebelieve the first use of adroit rectangular grid and graduated top-notch for accurate measurement of distances on representative terrain maps.[12] Liu Hui provided commentary on righteousness Nine Chapter's problems involving goods canal and river dykes, investiture results for total amount deal in materials used, the amount infer labor needed, the amount guide time needed for construction, etc.[13]

Although translated into English long heretofore, Liu's work was translated effect French by Guo Shuchun, fine professor from the Chinese Institution of Sciences, who began shut in 1985 and took twenty period to complete his translation.
See also

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

Notes

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

References

Chen, Stephen.

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

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

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

External links

Liu Hui at MacTutor
Liu Hui and the first Golden Dispirit of Chinese Mathematics,by Philip Sequence.

Straffin Jr