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How many mathematical laws can be found from Yang Hui's triangle?
Yang Hui was an outstanding mathematician and mathematical educator in the Southern Song Dynasty. Qian Guang, a native of Qiantang (present-day Hangzhou), was an ancient mathematician and mathematics educator in China, whose life experience is unknown. It can be inferred from the existing literature that Yang Hui worked as a local administrative officer in the Southern Song Dynasty, and he traveled all over Suzhou and Hangzhou, signing five kinds of mathematics books, with a total volume of 2 1 volume. He is the first mathematician in the world to draw a rich vertical and horizontal map and discuss its composition law. Together with Qin, Li Zhi and Zhu Shijie, they are called the four great mathematicians in Song and Yuan Dynasties. Yang Hui Triangle Yang Hui Triangle, also known as Jia Xian Triangle and Pascal Triangle, is a geometric arrangement of binomial coefficients in the triangle. 1, the numbers in each row are symmetrical, increasing gradually from 1, then decreasing and returning to 1. 2. The number of digits in row N is n..3 The sum of digits in row N is 2 (n- 1). Each number is equal to the sum of the left and right numbers in the previous line. This property can be used to write the whole Pascal triangle. 5. Connect the number 1 in the 2n+ 1 line with the number 3 in the 2n+2 line and the number 5 in the 2n+2 line, and the sum of these numbers is the 2n Fibonacci number. The sum of the number 2 in 2n row, the number 4 in 2n+ 1 row and the number 6 in 2n+2 row is 2n- 1 Fibonacci number. 6. The number of line n 1 is 1, the second number is 1×(n- 1), and the third number is1× (n-1) × (n-2)/ There are many mysteries waiting for you to explore. I wish you success. ...