Yang Hui: Difference between revisions

'''Yang Hui''' ({{zh|t=楊輝|s=杨辉|p=Yáng Huī}}, ca. 1238–1298), [[courtesy name]] '''Qianguang''' ({{lang|zh|謙光}}), was a Chinese mathematician and writer during the [[Song dynasty]]. Originally, from Qiantang (modern [[Hangzhou]], [[Zhejiang]]), Yang worked on [[magic square]]s, [[magic circle (mathematics)|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 mathematicianof [[Qin Jiushao]], another well-known Chinese mathematician.

The earliest extant Chinese illustration of '[[Pascal's triangle]]' is from Yang's book ''XiangjieXiángjiě JiuzhangJiǔzhāng Suànfǎ Suanfa'' ({{lang|zh|詳解九章算法}})<ref>Fragments of this book was retained in the Yongle Encyclopedia vol 16344, in British Museum Library</ref> 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]]<ref name="needham volume 3 134 137">Needham, Volume 3, 134-137.</ref> who expounded it around 1100 AD, about 500 years before Pascal. In hisHis book (now lost), known as ''Rújī Shìsuǒ'' ({{lang|zh|如積釋鎖}}) or ''Piling-up Powers and Unlocking Coefficients'', which iswas known through his contemporary mathematician [[Liu Ruxie]] ({{lang|zh|劉汝諧}}).<ref name="needham volume 3 137">Needham, Volume 3, 137.</ref> Jia described the method used as 'li cheng shi suo' (the tabulation system for unlocking binomial coefficients).<ref name="needham volume 3 137"/> It appeared again in a publication of [[Zhu Shijie]]'s book ''Jade Mirror of the Four Unknowns'' ({{lang|zh|四元玉鑒}}) of 1303 AD.<ref name="needham volume 3 134 135">Needham, Volume 3, 134-135.</ref>

Around 1275 AD, Yang finally had two published mathematical books, which were known as the ''XuguXùgǔ ZhaiqiZhāijī SuanfaSuànfǎ'' ({{lang|zh|續古摘奇算法}}) and the ''SuanfaSuànfǎ TongbianTōngbiàn BenmoBěnmò'' ({{lang|zh|算法通變本末}}, summarily called ''YangYáng HuiHuī SuanfaSuànfǎ'' {{lang|zh|楊輝算法}}).<ref name="needham volume 3 104">Needham, Volume 3, 104.</ref> In the former book, Yang wrote of arrangement of natural numbers around concentric and non concentric circles, known as [[magic circle (mathematics)|magic circles]] and vertical-horizontal [[diagram]]s of complex [[combinatorial]] arrangements known as [[magic squares]], providing rules for their construction.<ref name="needham volume 3 59 60">Needham, Volume 3, 59-60.</ref> In his writing, he harshly criticized the earlier works of [[Li Chunfeng]] and [[Liu Yi (mathematician)|Liu Yi]] ({{lang|zh|劉益}}), the latter of whom were both content with using methods without working out their theoretical origins or principle.<ref name="needham volume 3 104"/> Displaying a somewhat modern attitude and approach to [[mathematics]], Yang once said: