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Liu Hui

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Liu Hui
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{{about|the ancient mathematician|the modern politician|Liu Hui (politician)}}







factoids
225Lee & Tang.| birth_place = Zibo, Shandong| death_date = {{circa}} 295| death_place = | occupation = Mathematician, writer}}







factoids
}}{{Chinese-name|Liu}}Liu Hui ({{floruit|3rd century CE}}) was a Chinese mathematician and writer who lived in the state of Cao Wei during the Three Kingdoms period (220–280) of China. 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, in which he was possibly the first mathematician to discover, understand and use negative numbers. He was a descendant of the Marquis of Zi District (菑鄉侯) of the Eastern Han dynasty, whose marquisate is in present-day Zichuan District, Zibo, Shandong. He completed his commentary to the Nine Chapters in the year 263. He probably visited Luoyang, where he measured the sun's shadow.

Mathematical work

Along with Zu Chongzhi (429–500), Liu Hui was known as one of the greatest mathematicians of ancient China.Needham, Volume 3, 85-86 Liu Hui expressed all of his mathematical results in the form of decimal fractions (using metrological units), yet the later Yang Hui (c. 1238-1298 AD) expressed his mathematical results in full decimal expressions.Needham, Volume 3, 46.Needham, Volume 3, 85.Liu provided commentary on a mathematical proof of a theorem identical to the Pythagorean theorem.Needham, Volume 3, 22. 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".Needham, Volume 3, 95-96.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.Needham, Volume 3, 98-99. 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. In his commentaries on the Nine Chapters, he presented:
  • An algorithm for calculation of pi ({{pi}}) in the comments to chapter 1.Needham, Volume 3, 66. He calculated pi to 3.141024
< pi < 3.142074 with a 192 (= 64 × 3) sided polygon. Archimedes used a circumscribed 96-gon to obtain the inequality pi

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