How did Omar Khayyam’s work relate to Pascal’s triangle?

Created from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles.

French philosopher Blaise Pascal — Blaise Pascal Blaise Pascal, oil painting by an anonymous artist, c. 1650; in the Musée Carnavalet–Histoire de Paris, Paris. Pascal laid the foundation for probability theory.

Although Pascal’s triangle is named after the 17th-century French mathematician Blaise Pascal, the triangular arrangement of numbers used to determine binomial coefficients was studied centuries earlier by several mathematicians.

The Persian mathematician, astronomer, and poet Omar Khayyam investigated the remarkable pattern of these coefficients in the 11th century, long before Pascal’s work. While the triangle is often associated with Pascal in the West, it was also developed independently by Chinese mathematicians such as Jia Xian and Yang Hui, and it appeared in the 1303 work Siyuan yujian by Zhu Shijie, where it was already referred to as the "Old Method."1