Introduction to Jia Xian:
People in the Northern Song Dynasty completed the Nine Chapters of Yellow Emperor's Fine Grass in about 1050. The original book was lost, but its main contents were copied by Yang Hui's works (about13rd century), so it was handed down from generation to generation. Yang Hui's Detailed Explanation of Nine Chapters' Algorithms (126 1) has a diagram of "the origin of alchemy", which shows that "Jia Xian used this technique".
This is the famous "Jiaxian Triangle", or "Yang Hui Triangle". Jia Xian's "Method of Increasing, Multiplying and Opening" for higher-order square roots is also recorded in "Detailed Explanation of Algorithms in Chapter Nine".
Introduction to Jia Xian Triangle:
Jiaxian Triangle (Jiaxian Triangle) generally refers to Yang Hui Triangle and Yang Hui Triangle, which is a geometric arrangement of binomial coefficients in the triangle. In Europe, this watch is called Pascal Triangle.
Pascal (1623- 1662) discovered this rule in 1654, which was 393 years later than Yang Hui and 600 years later than Jia Xian. Yang Hui Triangle is one of the outstanding research achievements of ancient mathematics in China. It displays binomial coefficients graphically, and intuitively reflects some algebraic properties of combination numbers. It is a combination of discrete numbers and shapes.
Historical evolution of Jia-Xian triangle;
Jia Xian, a native of the Northern Song Dynasty, first used "Jia Xian Triangle" to calculate the higher-order root in 1050.
Yang Hui was born in Hangzhou in the Southern Song Dynasty. In his book "Detailed Explanation of Nine Chapters Algorithm" written by 126 1, he compiled a triangular table as shown above, which is called the Origin of Rooting, and explained that this table was quoted from the middle of 1 1 century (about AD 1050). Therefore, Yang Hui Triangle is also called "Jia Xian Triangle".
In Siyuan Jade Mirror (1303), Zhu Shijie, a mathematician in the Yuan Dynasty, developed the "A string triangle" into an "ancient seven-power diagram".
Italians call it the "tartaglia Triangle" in memory of Tattaglia, who discovered the solution of the cubic equation of one variable in16th century.
In Europe, after 1623, Pascal, a French mathematician, discovered Pascal's triangle at the age of 3 1.
Blaise Pascal's book The Arithmetic Trajectory of Triangle (1655) introduced this triangle. Pascal collected several results about it, solved some problems in probability theory and had a wide influence. Pierre Raymond demont (1708) and Abraham de Moivre (1730) both called this triangle Pascal.
Since the 20th century, foreign countries have gradually recognized that this achievement belongs to China, so there is a book called "China Triangle".