How did Jia Xian contribute to the early history of Pascal’s triangle?

In the 11th century, the Chinese mathematician Jia Xian devised a triangular representation of numbers that contained the binomial coefficients for equations up to the sixth degree. This arrangement, now widely known as Pascal’s triangle, was developed by Jia as part of his work on methods for extracting roots of polynomials and solving algebraic equations.123

Jia’s contribution was foundational to the history of this mathematical structure. His triangular configuration allowed for the systematic calculation of coefficients, which he utilized alongside algorithms for root extraction. While the triangle is named after the 17th-century French mathematician Blaise Pascal, who discovered it independently, Jia’s earlier work established the pattern's utility in algebra centuries prior. His methods were later studied and popularized in China by Yang Hui in the 13th century, leading to the triangle often being referred to as the Yang Hui triangle in that region.132