The binomial theorem was originally used to open higher powers. In China, Nine Chapters Arithmetic, written in 1 century AD, put forward the world's earliest general program for finding the square root and square root of multiple positive integers.

1 65438+In the middle of the 20th century, Jia Xian gave the "original map of cholesky decomposition" (as shown in figure1) in his unlock calculation book, which met the needs of more than three square roots. This graph is a binomial coefficient table of the sixth power. However, Jia Xian did not give the general formula of binomial coefficient, so he failed to establish the binomial theorem of general positive integer power.

In Arabia, in the 10 century, Al Karadji already knew the construction method of binomial coefficient table: any number in each column is equal to the number in the same row in the previous column plus the number above it. 11~12nd century, Omar Hagham extended Indian roots and root operations to any higher order, so he studied binomial expansion of higher order.

/kloc-in the 3rd century, Nasser al-Din gave an approximate formula of higher-order roots in his "Integration of Computing Board and Sand Table Algorithm" and applied it to the binomial coefficient table. /kloc-in the 0/5th century, Al Cassie introduced the method of arbitrary high-order opening in Key to Arithmetic.

A binomial coefficient table up to the ninth power is given, and two books give a binomial coefficient table, which has the same shape as Jia Xian's triangle. /kloc-In the 6th century, many mathematicians had binomial coefficient tables in their books.