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Jia Xian triangle (Pascal's triangle) using rod numerals, as depicted in a publication of Zhu Shijie in 1303 AD.

Jia Xian (贾宪) (approximately 1010-1070 AD) was a Chinese mathematician of the Song Dynasty, first half of 11th century. Jia Xian studied under mathemtician Chu Yan. Jia Xian invented Jia Xian triangle around the first half of 11th century, about 500 years before Pascal. Jia Xian used it as a tool to find the square roots and cubic roots. The original book by Jia Xian titled "Shi Suo Suan Shu" was lost, however Jia's method was expounded in detail by Yang Hui, who explicitly acknowledged that "my method of finding square and cubic root was based on Jia Xian method in Shi Suo Suan Shu."^[1]

References

1. ^ Wu Wenjun chief ed, The Grand Series of History of Chinese Mathematics Vol 5 Part 2, chapter 1, Jia Xian

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