The most outstanding achievement of Yang Hui's life is to draw a wealth of vertical and horizontal maps, and discuss their composition rules. Speaking of this achievement of Yang Hui, we have to start with an accidental event.
One day, Yang Hui, a local official in Taizhou, went out for a cruise. On the way, the gong cleared the way in front, and the official behind the house rose in the middle, which was very imposing. Walking, I saw the boring gong that was escorting stopped, and there was a loud cry from the child in front, followed by a fierce reprimand from the chief. Yang Hui asked what was going on and sent someone to report: "The child won't let him go, saying that he won't let him go until he finishes the problem, or he will take a detour."
When Yang Hui saw the interest, he stepped out of the sedan chair and came to the front. The village chief quickly said, "Did you coax the child away?"
Yang Hui touched the child's head and said, "Why not let my official pass through here?"
The child replied, "it's not that I'm not allowed to pass." I'm afraid you stepped on my formula and I can't remember it again. "
"What formula?"
"That is, the numbers of 1 to 9 are arranged in three rows. Whether vertical, horizontal or oblique, the result is equal to 15. This afternoon, our husband asked us to do this problem well. I am counting the key points. "
Yang Hui quickly squatted down and looked at the child's formula carefully. I think this man has met somewhere. When you think about it carefully, it turned out to be mentioned in "Da Dai Li Ji" edited by Dade, a scholar of the Western Han Dynasty. Yang Hui and the children quickly calculated together. It was not until after noon that they breathed a sigh of relief. The results came out and they checked it again. The result is 15, standing up.
Yang Hui returned home, pondered it over and over again, fiddled with these figures on the table whenever he had time, and finally found a rule. First, nine numbers are arranged in three rows obliquely from big to small, then 9 and 1 are reversed, 7 on the left and 3 on the right are reversed, and finally, 4, 2, 6 and 8 on the four corners are moved outward and arranged in three rows, thus forming the Nine palace map. Later, Yang Hui sorted out this kind of problems scattered in predecessors' works and circulated among the people, and got many similar pictures, such as Five-Five, Six-Six, Evolution, Yi Tu, Nine-Nine and Hundred-Child. Yang Hui has always called these graphs vertical and horizontal graphs, and wrote them into his own mathematical book "Algorithm for Continuation of the Ancient" at 1275, which was handed down to later generations. He is the first mathematician in the world to give such a rich vertical and horizontal diagram and discuss its composition law.
Yang Hui is not only an excellent mathematician, but also an outstanding mathematics educator. He devoted his life to the education and popularization of mathematics, and many of his works were written for the education and popularization of mathematics. The book "The Background of Algorithm Change" contains Yang Hui's "learning plan" specially formulated for beginners, which embodies Yang Hui's thoughts and methods of mathematics education.