# give me Yang Hui imformation!!!!

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Yang Hui courtesy name Qianguang was a Chinese mathematician from Qiantang (modern Hangzhou), Zhejiang province during the late Song Dynasty (960-1279 AD). Yang worked on magic squares and binomial theorem, and is best known for his contribution of presenting &#39;Yang Hui&#39;s Triangle&#39;. This triangle was the same as Pascal&#39;s Triangle, discovered independently by Yang and his predecessor Jia Xian (贾宪). Yang was also a contemporary to the other famous mathematician Qin Jiushao.

The earliest extant Chinese illustration of &#39;Pascal&#39;s Triangle&#39; is from Yang&#39;s book Xiangjie Jiuzhang Suanfa (详解九章算法) of 1261 AD, although it existed beforehand.[1] A Chinese mathematician known as Jia Xian expounded it around 1100 AD, described in his book (now lost) known as Ruji Shisuo (如积释锁) or Piling-up Powers and Unlocking Coefficients, which is known through his contemporary mathematician Liu Ruxie (刘汝谐).[2] Jia described the method used as &#39;li cheng shi suo&#39; (the tabulation system for unlocking binomial coefficients).[2] It appeared again in a publication of Zhu Shijie&#39;s book Jade Mirror of the Four Unknowns (四元玉鉴) of 1303 AD.[3]

Around 1275 AD, Yang finally had two other mathematical books of his published, which were known as the Xugu Zhaiqi Suanfa (续古摘奇算法) and the Suanfa Tongbian Benmo (算法通变本末).[4] In the former book, Yang wrote of vertical-horizontal diagrams of complex combinatorial arrangements known as &#39;magic squares&#39;, providing rules for their construction.[5] In his writing, he harshly criticized the earlier works of Li Chunfeng and Liu Yi (刘益), the latter of whom were both content with using methods without working out their theoretical origins or principle.[4] Displaying a somewhat modern attitude and approach to mathematics, Yang once said:

The men of old changed the name of their methods from problem to problem, so that as no specific explanation was given, there is no way of telling their theoretical origin or basis.[4]

In his written work, Yang provided theoretical proof for the proposition that the complements of the parallelograms which are about the diameter of any given parallelogram are equal to one another.[4] This was the same idea expressed in Euclid&#39;s forty-third proposition of his first book, only Yang used the case of a rectangle and gnomon.[4] There were also a number of other geometrical problems and theoretical mathematical propositions posed by Yang that were strikingly similar to the Euclidean system.[6] However, the first books of Euclid to be translated into Chinese was by the cooperative effort of Matteo Ricci and Xu Guangqi in the early 17th century.[7

Yang&#39;s writing represents the first in which quadratic equations with negative coefficients of &#39;x&#39; appear, although he attributes this to the earlier Liu Yi.[8] Yang was also well known for his ability to manipulate decimal fractions. When he wished to multiply the figures in a rectangular field with a breadth of 24 paces 3 4⁄10 ft. and length of 36 paces 2 8⁄10, Yang expressed them in decimal parts of the pace, as 24.68 X 36.56 = 902.3008.[9]

2007-10-12 17:43:58 補充：

楊輝（約1238年－約1298年），字謙光，錢塘（今浙江杭州）人，是中國南宋時的偉大數學家。楊輝生於宋理宗嘉熙二年(約1238年)，終於元成宗大德二年（約1298年）。他著有《詳解九章算經》12卷、《日用演算法》2卷、《乘除通變算寶》3卷、《田畝比類乘除捷法》2卷、《續古摘奇演算法》2卷及《九章演算法篡類》等多本演算法的著作。另一方面，他在宋度宗咸淳年間的兩本著作裡，亦有提及當時南宋的土地價格。這些資料亦對後世史學家瞭解南宋經濟發展有很重要的幫助。

2007-10-12 17:44:46 補充：

楊輝在著作中收錄了不少現已失傳的、古代各類數學著作中很有價值的算題和演算法，保存了許多十分寶貴的宋代數學史料。他對任意高次冪的開方計算、二項展開式、高次方程的求解、高階等差級數、縱橫圖等問題，都有精到的研究。楊輝十分留心數學教育，並在自己的實踐中貫徹其教育思想。楊輝更對於垛積問題(高階等差級數)及幻方作過詳細的研究。由於他在他的著作裡提及過賈憲對二項展開式的研究，所以「賈憲三角」又名「楊輝三角」。

2007-10-12 17:44:55 補充：

這比歐洲於17世紀的同類型的研究「帕斯卡三角形」早了差不多五百年。在《乘除通變算寶》中，楊輝創立了「九歸」口訣，介紹了籌算乘除的各種速演算法等等。這些在中國數學史上，都佔有重要的地位。在《續古摘奇演算法》中，楊輝列出了各式各樣的縱橫圖（幻方），它是宋代研究幻方的最重要的著述。楊輝對我國古代的幻方，不僅有深刻的研究，而且還創造了一個圓形幻方

Source(s): internet