Jia Xian

Source: Wikipedia, the free encyclopedia.
In this Chinese name, the family name is Jia.
Jia Xian triangle (Pascal's triangle) using rod numerals, as depicted in a publication of Zhu Shijie in 1303 AD.
Yang Hui referred to Jia Xian's Shi Suo Suan Shu in the Yongle Encyclopedia

Jia Xian (simplified Chinese: 贾宪; traditional Chinese: 賈憲; pinyin: Jiǎ Xiàn; Wade–Giles: Chia Hsien; ca. 1010–1070) was a Chinese mathematician from Kaifeng of the Song dynasty. He described Pascal's triangle during the 11th century.

Biography

According to the history of the Song dynasty, Jia was a palace

cubic roots. The original book by Jia entitled Shi Suo Suan Shu was lost; however, Jia's method was expounded in detail by Yang Hui, who explicitly acknowledged his source: "My method of finding square and cubic roots was based on the Jia Xian method in Shi Suo Suan Shu."[1] A page from the Yongle Encyclopedia
preserved this historic fact.

Jia Xian's additive-multiplicative method implemented the "Horner" rule.[2]

Additive-multiplicative method of square-root extraction

Jia Xian additive-multiplicative square-root extraction
Jia Xian additive-multiplicative square-root extraction

Additive-multiplicative method of cubic-root extraction

Jia Xian add-multiply method for cubic roots
Jia Xian add-multiply method for cubic roots


References

  1. ^ Wu Wenjun chief ed, The Grand Series of History of Chinese Mathematics Vol 5 Part 2, chapter 1, Jia Xian
  2. ^ Jean-Claude Martzloff, A History of Chinese Mathematics Springer, p142
  • J-C Martzloff, A history of Chinese mathematics (Berlin-Heidelberg, 1997).
  • J-C Martzloff, Histoire des mathématiques chinoises (Paris, 1987).
  • B Qian, History of Chinese mathematics (Chinese) (Peking, 1981).
  • K Chemla, Similarities between Chinese and Arabic mathematical writings I : Root extraction, Arabic Sci. Philos. 4 (2) (1994), 207-266.
  • S Guo, Preliminary research into Jia Xian's Huangdi Jiuzhang Suanjing Xicao (Chinese), Studies in the History of Natural Sciences 7 (4) (1988), 328 -334.
  • S Guo, Jia Xian, in Du Shiran (ed.), Zhongguo Gudai Kexuejia Zhuanji (Biographies of Ancient Chinese Scientists) (Beijing, 1992), 472 -479.
  • R Mei, Jia Xian's additive-multiplicative method for the extraction of roots (Chinese), Studies in the History of Natural Sciences 8 (1) (1989), 1 -8.

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