Yang Hui

Yang Hui (simplified Chinese: 杨辉; traditional Chinese: 楊輝; pinyin: Yáng Huī, ca. 1238–1298), courtesy name Qianguang (謙光), was a late-Song dynasty Chinese mathematician 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.

The earliest extant Chinese illustration of 'Pascal's Triangle' is from Yang's book Xiangjie Jiuzhang Suanfa (詳解九章算法) 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 (如積釋鎖) or Piling-up Powers and Unlocking Coefficients, which is known through his contemporary mathematician Liu Ruxie (劉汝諧). 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 (四元玉鑒) of 1303 AD.

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