Yang Hui

Yang Hui (, ca. 1238–1298), courtesy name Qianguang, was a Chinese mathematician and writer during the Song dynasty. Originally, from Qiantang (modern Hangzhou, Zhejiang), Yang worked on magic squares, magic circles and the binomial theorem, and is best known for his contribution of presenting Yang Hui's Triangle. This triangle was the same as Pascal's Triangle, discovered by Yang's predecessor Jia Xian. Yang was also a contemporary to the other famous mathematician Qin Jiushao. Written work The earliest extant Chinese illustration of 'Pascal's triangle' is from Yang's book Xiangjie Jiuzhang Suanfa of 1261 AD, in which Yang acknowledged that his method of finding square roots and cubic roots using "Yang Hui's Triangle" was invented by mathematician Jia Xian who expounded it around 1100 AD, about 500 years before Pascal. In his book (now lost) known as Rújī Shìsuǒ or Piling-up Powers and Unlocking Coefficients, which is known through his contemporary mathematician Liu Ruxie. Jia described the method used as 'li cheng shi suo' (the tabulation system for unlocking binomial coefficients). It appeared again in a publication of Zhu Shijie's book Jade Mirror of the Four Unknowns of 1303 AD. Around 1275 AD, Yang finally had two published mathematical books, which were known as the Xugu Zhaiqi Suanfa and the Suanfa Tongbian Benmo (, summarily called Yang Hui suanfa ). In the former book, Yang wrote of arrangement of natural numbers around concentric and non concentric circles, known as magic circles and vertical-horizontal diagrams of complex combinatorial arrangements known as magic squares, providing rules for their construction. In his writing, he harshly criticized the earlier works of Li Chunfeng and Liu Yi, the latter of whom were both content with using methods without working out their theoretical origins or principle. 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.