1. Yang Hui triangle, the geometric arrangement of binomial coefficients in the triangle, appeared in the book "Detailed explanation of nine chapters" written by Yang Hui, a mathematician in the Southern Song Dynasty in China +026 1. In Europe, Pascal (1623- 1662) discovered this rule in 1654, so this table is also called Pascal triangle. Pascal's discovery was 393 years later than Yang Hui's and 600 years later than Jia Xian's.

Yang Hui Triangle is a great achievement in the history of Chinese mathematics.

Pascal triangle, also known as Jia Xian triangle, Yang Hui triangle, khayyam triangle and Pascal triangle, is a way of writing binomial coefficient, which looks like a triangle. It first appeared in China, and was named after Yang Hui's Nine Chapters of Arithmetic in the Southern Song Dynasty. Yang Hui's explanation in the book is quoted from Jia Xian's Unlocking Arithmetic, so it is also called Jia Xian Triangle.

Second, the basic introduction

Simply put, it is the coefficient problem after the power operation of the sum of two unknowns, such as (x+y)? =x？ +2xy+y？ This coefficient is 1, 2, 1. This is a line of Yang Hui's triangle, three times and four times. Look at the coefficient of each term, and you will understand the truth.

This is Yang Hui Triangle, also called Jia Xian Triangle, and Pascal Triangle abroad. What he and we study most closely now is the coefficient law of binomial power expansion. As shown in the figure, in Jiaxian Triangle, the third number in the third row just corresponds to the square formula of the sum of two numbers (which will not be explained here).

Three. Basic definition

The nth layer of Yang Hui triangle (the top layer is called layer 0, line 1, and the nth layer is line n+ 1, where n is a natural number containing 0) just corresponds to the coefficient of binomial expansion. For example, the second layer 1 2 1 is a binomial with power exponent of 2.

Expansion form

The coefficient of.