Yang Hui was a famous mathematician in the Southern Song Dynasty, what did he do about mathematics?

Yang Hui was a famous mathematician in the Southern Song Dynasty, he was born in Hangzhou, Zhejiang, and stayed almost in his hometown of Suzhou and Hangzhou while serving in the imperial court. Yang Hui is an upright person and is deeply loved by the common people, and he has studied mathematics in this areaLater generations will join him with Qin Jiushao, Li Zhi, and Zhu Shijie as the "Four Masters of Song and Yuan Mathematics".The well-known Yang Hui Triangle is his most important research achievementYang Hui left a large number of works on mathematics in his life, such as "Nine Chapters of Algorithm", "Daily Algorithm", "Multiplication and Division", and other books are the algorithm theories he summarized according to the places where ordinary people need to use arithmetic in their lives, so as to help people quickly calculate their needs. <>

Yang Hui can be said to be the first person in the world to arrange vertical and horizontal graphs, and he recorded the algorithm of vertical and horizontal graphs in detail in the "Continuation of the Ancient Picking Strange Algorithm", which made great contributions to the world's arithmetic. During the Southern Song Dynasty, commerce and handicrafts gradually developed, and the social economy also improved steadily. In fact, there were more practical calculation books in the late Tang Dynasty, but by the Song Dynasty, most of these books had been lost.

Yang Hui continued to innovate on the basis of summarizing the research of mathematicians in the previous dynasties, and made great contributions to Chinese arithmetic. Yang Hui's re-improved multiplication and division calculation technology has provided users with a lot of benefits, making the operation easier, and the calculation speed and accuracy have been further improved. Yang Hui not only improved the algorithm, but also put forward some practical and easy-to-remember operation formulas, such as "return to ten", "return to add from top", etc.

Yang Hui is not only a mathematician but also an excellent educator, he has dedicated his life to the great cause of mathematics education, and we should learn from his spirit of dedication.

Yang Hui has five kinds of mathematical works in 21 volumes, including nine chapters of algorithms, daily algorithms, multiplication and division, perfect addition method, vertical and horizontal diagrams, and stacking techniques; multiplication and division algorithms and prime numbers; "Yang Hui.

Triangle" and so on.

Yang Hui was the first mathematician in the world to exhaust rich vertical and horizontal graphs and discuss the laws of their composition, and also demonstrated the arc vector formula, and was also one of the four masters of mathematics in the Song and Yuan dynasties.

He has written books such as "Detailed Explanation of Nine Chapters of Algorithm", "Daily Algorithm", "Multiplication and Division", "Multiplication and Division", "Multiplication and Division". Yang Hui summed up the algorithm theory according to the daily needs of the operation to help the people calculate the needs. It is worth mentioning that Yang Hui is the world's first vertical and horizontal chart, and summed up the theoretical knowledge of the composition of laws from it, which promotes the process of arithmetic in the world, and has high practical significance.

Yang Hui Triangle is a mathematician of the Southern Song Dynasty of China, with a total of 55 numbers.

Yang Hui Triangle's intermediary hall is chaotic:

The most essential feature of the Yang Hui Triangle is that the two hypotenuses of the Song Fu Leak are composed of the number 1, while the rest of the numbers are equal to the sum of the two numbers on its shoulder. In fact, ancient Chinese mathematicians were far ahead in many important fields of mathematics. The history of ancient Chinese mathematics once had its own glorious chapter, and the discovery of Yang Hui's triangle is a very wonderful page.

Yang Hui, whose name is Qianguang, was born in Hangzhou during the Northern Song Dynasty. In his 1261 book "A Detailed Explanation of the Nine Chapters of Algorithms", he compiled a table of triangular numbers shown above, which he called the "origin of the square method" diagram. And such a triangle is often used in our Olympiad competitions, and the simplest thing is to ask you to find the pattern.

The Yang Hui triangle, also known as the Jia Xian triangle, Pascal triangle, and Pascal triangle, is a geometric arrangement of binomial coefficients in a triangle. The Yang Hui triangle also corresponds to the coefficients of the binomial theorem. The coefficients of the two-field rotten term n corresponding to the n + 1 row of Yang Hui's triangle.

Yang Hui, whose name is Qianguang, was born in Hangzhou during the Southern Song Dynasty. In his 1261 book "Detailed Explanation of the Nine Chapters of Algorithms", he compiled the table of triangle numbers shown above, which he called the "origin of the method of opening squares", and explained that this table was quoted from Jia Xian's "Arithmetic of Unlocking Locks" in the middle of the 11th century (about 1050 AD), and painted the "ancient seven-power diagram". Therefore, the Yang Hui Triangle is also known as the "Jia Xian Triangle".

Yang Hui, one of the four masters of mathematics in the Song and Yuan dynasties, was the first mathematician in the world to exhaust rich vertical and horizontal diagrams and discuss the laws of their composition.

Speaking of Yang Hui's achievement, we have to start with an accidental trivial matter.

Later, Yang Hui sorted out the relevant issues scattered in the writings of his predecessors and circulated among the people, and obtained many similar diagrams, such as "Five-Five Diagrams", "Six-Six Diagrams", "Derivative Diagrams", "Easy Number Diagrams", "Ninety-Nine Diagrams", "Hundred Son Diagrams" and so on.

Yang Hui referred to these graphs as vertical and horizontal graphs, and in 1275 he wrote them into his mathematical work "Continuing the Ancient Strange Algorithm", which was passed down to future generations. But for a long time, people have been accustomed to treating it as a purely mathematical game and not giving it the attention it deserves.

With the development of modern combinatorics, vertical and horizontal graphs have shown more and more powerful vitality, and have found a place in the fields of graph theory, combinatorial analysis, countermeasure theory, and computer science.

Yang Hui can be said to be the first mathematician in the world to give such a rich vertical and horizontal diagram and discuss the laws of its composition.

In addition to this achievement, Yang Hui also has a major contribution, which is the "Yang Hui Triangle".

Once, Yang Hui got a copy of "The Yellow Emperor's Nine Chapters of Algorithm Fine Grass", which was written by Jia Xian, a few scholars in the Northern Song Dynasty. There are many remarkable achievements in this, such as Jia Xian's drawing of a picture, which is called "the origin map of the opening method". In the West, it wasn't until the 16th century that a similar figure was drawn on the cover of a book.

The French mathematician Basgar discussed the properties of this figure in detail in 1654, so it is also called the "Bascan triangle" in the West.

In addition to the above achievements, Yang Hui also wrote books such as "Daily Algorithm", "Multiplication and Division" and "Multiplication and Division", which provided extremely important information for later generations to understand the mathematical landscape at that time.

Several of Yang Hui's works have greatly enriched the treasure house of ancient mathematics in China and made outstanding contributions to the development of mathematical science.

Write out the Yang Hui Triangle.

Concern. Many students will think that mathematics is boring, the reason is that they do not know how to count and miss the purpose of learning mathematics when they learn mathematics. If you understand the use of mathematics, your interest in learning will be different.

Today, let's learn together to see what is the Yang Hui Triangle, which is suitable for middle school students.

Ask questions. Let's think about a question first, in ancient times, if you want to draw a square piece of land, the area of this land is 10 square meters, what should you do? In other words, it is the numerical solution to be solved.

Note: In ancient times, there were no calculators, only paper and pen. After today's lesson, we will be able to comprehend the wisdom of the ancients.

What is the Yang Hui Triangle.

Line 0: A number 1 is formed. (Note: Some textbooks refer to this as line 1, which is just a difference in definition and does not affect our learning).

Row 1: Two numbers 1.

From line 2: the first and last digits are 1, and the other digits are equal to the sum of the two numbers on the shoulder. For example, the 2 in line 2 is equal to the sum of the two 1s in line 1 (2=1+1).

It gives the general formula for line n-1 and line n, if you haven't learned the permutation and combination of this formula, put it first, this mark means:

Characteristics of the Yang Hui Triangle.

There are many interesting features of the Yang Hui Triangle, some of which are listed below:

The sum of the digits in line nth is equal to.

The number in line nth is exactly the binomial coefficient, e.g. the coefficient is exactly 1, 2, 1.

The number in each row is exactly yes, e.g. 121=, liter in line 2 or 1331= in line 3. Why is it so coincidental? Just take a look at it.

Each number is equal to the sum of the two numbers on the shoulder, which is just right to introduce the formula.

This formula will definitely be talked about when learning permutations and combinations, and if you prove it, you can directly use the definition, and this formula will not be proved here.

Answer: Yang Hui, a mathematician in the Song Dynasty in China, can draw a picture according to the relationship between the characters.