A possible likeness of Liu Hui on a Chinese postage stamp

This is a Chinese name; the family name is 劉 (Liu). A postage stamp is an adhesive paper evidence of pre-paying a fee for postal services Personal Names in Chinese culture follow a number of conventions different from those of personal names in Western cultures. Chinese family name is one of the hundreds or thousands of Family names that have been historically used by Han Chinese and Sinicized Chinese ethnic Liu is a common Chinese family name. The Transliteration Liu can represent several different surnames written in different Chinese characters

Liu Hui (traditional Chinese: 劉徽; simplified Chinese: 刘徽; pinyin: Liú Huī, fl. Pinyin, more formally Hanyu pinyin, is the most common Standard Mandarin Romanization system in use 3rd century) was a Chinese mathematician who lived in the Wei Kingdom. The 3rd century is the period from 201 to 300 in accordance with the Julian calendar in the Christian / Common Era. China ( Wade-Giles ( Mandarin) Chung¹kuo² is a cultural region, an ancient Civilization, and depending on perspective a National A mathematician is a person whose primary area of study and research is the field of Mathematics. Cao Wei ( was one of the empires that competed for control of China during the Three Kingdoms period In 263 he edited and published a book with solutions to mathematical problems presented in the famous Chinese book of mathematics known as The Nine Chapters on the Mathematical Art. Events By Place Roman Empire The Goths invade Ephesus and destroy city and temple The Nine Chapters on the Mathematical Art ( is a Chinese Mathematics book composed by several generations of scholars from the 10th&ndash2nd century BC and

Mathematical work

Liu was one of the first mathematicians known to leave roots unevaluated, giving more exact results instead of approximations. Along with Zu Chongzhi, they were among the greatest mathematicians of the ancient world. Zu Chongzhi ( 429–500 Courtesy name Wenyuan (文遠 was a prominent Chinese mathematician and astronomer during the Liu ^[1] Liu Hui expressed all of his mathematical results in the form of decimal fractions (using metrological units), yet the later Yang Hui (c. Measurement is the process of estimating the magnitude of some attribute of an object such as its length or weight relative to some standard ( unit of measurement) such as Yang Hui ( ca 1238–1298 Courtesy name Qianguang (谦光 was a Chinese Mathematician from Qiantang (modern Hangzhou 1238-1298 AD) expressed his mathematical results in full decimal expressions. ^[2][3] He also provided commentary on the mathematical proof that is identical to the Pythagorean theorem of the Greek Pythagoras (c. In Mathematics, the Pythagorean theorem ( American English) or Pythagoras' theorem ( British English) is a relation in Euclidean geometry The Greeks ( Greek: Έλληνες) are a Nation and Ethnic group native to Greece, Cyprus and neighbouring regions "Pythagoras of Samos" redirects here For the Samian statuary of the same name see Pythagoras (sculptor. 580 BC-500 BC). Events and trends 589 BC — Apries succeeds Psammetichus II as king of Egypt. ^[4] Liu Hui 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". ^[5] In terms of the treatment of plane areas and solid figures, Liu Hui was one of the greatest contributors to 'empirical' solid geometry. A central concept in Science and the Scientific method is that all Evidence must be empirical, or empirically based that is dependent on evidence For example, he figured out that a wedge with rectangular base and both sides sloping could be broken down into a pyramid and a tetrahedral wedge. A tetrahedron (plural tetrahedra) is a Polyhedron composed of four triangular faces three of which meet at each vertex. ^[6] He also figured out that a wedge with trapezoid base and both sides sloping could be made to give two tetrahedral wedges separated by a pyramid. A trapezoid (in North America or a trapezium (in Britain and elsewhere is a Quadrilateral (a closed plane shape with four linear sides that has at least one ^[6]

In his commentaries on the Jiuzhang suanshu, he presented (among other things):

• an estimate of π in the comments to chapter 1. The Nine Chapters on the Mathematical Art ( is a Chinese Mathematics book composed by several generations of scholars from the 10th&ndash2nd century BC and IMPORTANT NOTICE Please note that Wikipedia is not a database to store the millions of digits of π please refrain from adding those to Wikipedia as it could cause technical problems ^[7] He estimated pi to 3. 141024 with a 192 (= 2⁵ × 6) sided polygon and later calculated pi as 3. In Geometry a polygon (ˈpɒlɨɡɒn ˈpɒliɡɒn is traditionally a plane figure that is bounded by a closed path or circuit 14159 by using a 3072 (= 2⁹ × 6) sided polygon. ^[8] He suggested that 3. 14 was a good approximation. His estimation is made with a method similar to the Greek Archimedes of 250 BC who had used a 96 (= 2⁴ × 6) sided polygon, but with a decimal fraction at 3. Archimedes of Syracuse ( Greek:) ( c. 287 BC – c 212 BC was a Greek mathematician, Physicist, Engineer 142704, Liu Hiu's was a bit more accurate than Archimedes' (3. 1428). ^[8]Incidently, Luihui also obtain another value for π as 3. 142704, but he commented that this value was too large, and picked the first three digits of π=3. 141024 ~3. 14 and put it in to a fraction form π=. Nine Chapters had used the value 3 for the π formula, but Zhang Heng (78-139 AD) had previously estimated it to the square root of 10;
• Gaussian elimination;
• Cavalieri's principle to find the volume of a cylinder. The Nine Chapters on the Mathematical Art ( is a Chinese Mathematics book composed by several generations of scholars from the 10th&ndash2nd century BC and Zhang Heng ( (CE 78–139 was an astronomer, mathematician, inventor, geographer, cartographer, artist, poet Year 78 was a Common year starting on Thursday (link will display the full calendar of the Julian calendar. In Linear algebra, Gaussian elimination is an efficient Algorithm for solving systems of linear equations, to find the rank of a matrix Bonaventura Francesco Cavalieri (in Latin, Cavalerius) ( 1598 - November 30, 1647) was an Italian mathematician ^[9]

The commentaries often include explanations why some methods work and why others do not. Although his commentary was a great contribution, some answers had slight errors which was later corrected by the Tang mathematician and Taoist believer Li Chunfeng. The Tang Dynasty ( Middle Chinese: dhɑng (June 18 618&ndashJune 4 907 was an imperial dynasty of China preceded by the Sui Dynasty and followed by Li Chunfeng ( 602–670 was a Chinese mathematician, Astronomer, and Historian who was born in today's Baoji Shaanxi during the Sui

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. The Sea Island Mathematical Manual or Haidao suanjing (海岛算经 was written by the Chinese mathematican Liu Hui of the Three Kingdoms Surveying is the technique and science of accurately determining the terrestrial or three-dimensional space Position of points and the distances and angles between This book contained many practical problems of geometry, including the measurement of the heights of Chinese pagoda towers. The Chinese Pagoda is a Landmark in Birmingham, England. It is a stone carving of a Chinese pagoda, carved in Fujian, China ^[10] 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". ^[11] With this, the following cases are considered in his work:

• The measurement of the height of an island opposed to its sea level and viewed from the sea^[11]
• The height of a tree on a hill ^[11]
• The size of a city wall viewed at a long distance ^[11]
• The depth of a ravine (using hence-forward cross-bars)^[11]
• The height of a tower on a plain seen from a hill ^[11]
• The breadth of a river-mouth seen from a distance on land ^[11]
• The depth of a transparent pool ^[11]
• The width of a river as seen from a hill ^[11]
• The size of a city seen from a mountain, ^[11]

Liu Hui's information about surveying was known to his contemporaries as well. Mean sea level (MSL is the average (mean height of the Sea, with reference to a suitable reference surface A ravine is a very small Valley, which is often the product of Streamcutting Erosion. In Optics, transparency (also called pellucidity) is the Material property of allowing The cartographer and state minister Pei Xiu (224–271) outlined the advancements of cartography, surveying, and mathematics up until his time. Cartography or mapmaking (in Greek chartis = map and graphein = write has been an integral part of the human story for a long time (maybe 8000 years Pei Xiu (224&ndash271 was a minister geographer, and cartographer of the Kingdom of Wei during the Three Kingdoms Period of China This included the first use of a rectangular grid and graduated scale for accurate measurement of distances on representative terrain maps. Grid references define locations on Maps using Cartesian coordinates. ^[12]

Liu Hui provided commentary on the Nine Chapter's problems involving the building of 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. Canals are artificial channels for water There are two types of canals water conveyance canals which are used for the conveyance and delivery of water and Waterways LeveeEmbankmentDitch A dike (or dyke) levee, levée, embankment, floodbank or stopbank is a natural or artificial ^[13]

Although translated into English long beforehand, Liu's work has been translated into French by Guo Shuchun, a professor from the Chinese Academy of Sciences, who began this work in 1985 and took twenty years to complete it. French ( français,) is a Romance language spoken around the world by 118 million people as a native language and by about 180 to 260 million people The Chinese Academy of Sciences ( CAS) ( formerly known as Academia Sinica (not to be confused with the Republic of China 's (Taiwan Academia

See also

• Liu Hui's π algorithm
• The Sea Island Mathematical Manual
• History of mathematics
• History of geometry
• List of Chinese people
• History of China
• Chinese mathematics

Notes

References

• Chen, Stephen. "Changing Faces: Unveiling a Masterpiece of Ancient Logical Thinking. " South China Morning Post, Sunday, January 28, 2007. The South China Morning Post, together with its Sunday edition the Sunday Morning Post, is an English-language Newspaper of Hong
• Guo, Shuchun, "Liu Hui". Encyclopedia of China (Mathematics Edition), 1st ed. The Encyclopedia of China ( "China Great Encyclopedia" is the first large-entry modern Encyclopedia in the Chinese language.
• Hsu, Mei-ling. "The Qin Maps: A Clue to Later Chinese Cartographic Development," Imago Mundi (Volume 45, 1993): 90-100.
• Needham, Joseph & C. Cullen (Eds. ) (1959). Science and Civilisation in China: Volume III, section 19. Cambridge University Press. ISBN 0-521-05801-5.
• Needham, Joseph (1986). Science and Civilization in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth. Taipei: Caves Books, Ltd.
• Needham, Joseph (1986). Science and Civilization in China: Volume 4, Physics and Physical Technology, Part 3, Civil Engineering and Nautics. Taipei: Caves Books Ltd.

External links

• Liu Hui at MacTutor

This article contains Chinese text. Without proper rendering support, you may see question marks, boxes, or other symbols instead of Chinese characters. Mojibake is the happenstance of incorrect unreadable characters (garbage characters shown when Computer software fails to render a text correctly according to its associated A Chinese character, also known as a Han character ( is a Logogram used in writing Chinese (hanzi Japanese (