Qin's most important mathematical achievements are "the total number of large derivatives", that is, the first congruence group solution, and "positive and negative cholesky decomposition", that is, the numerical solution of higher-order equations. These achievements occupy a prominent position in the history of medieval mathematics.
In the Chu-Han War, on one occasion, Han Xin, a general under Liu Bang, and Li Feng, a general under Xiang Yu, the king of Chu, fought. After a bitter battle, the Chu army was defeated and retreated to the camp. The Han army also killed or injured four or five hundred people, so Han Xin reorganized his military forces and returned to the base camp.
Just as the Han army came to a hillside, suddenly a rear army came to report that Chu cavalry was coming after it. I saw the dust flying in the distance and the sound of ShaSheng was deafening. The Han army was very tired, and then the team was in an uproar.
Han Xin's military forces arrived at the top of the slope and saw that the enemy was riding less than 500, so they quickly ordered the troops to meet them. He ordered three soldiers in a row and ended up with two more; Then he ordered the soldiers to line up five times, and as a result, there were three more; He ordered a platoon of seven soldiers, only to get two more.
Han Xin immediately announced to the soldiers: Our army 1073 Warriors, with less than 500 enemy troops. If we are condescending, we will be outnumbered.
The Han army believed in the commander-in-chief, and now it believes that Han Xin is a "fairy"? "SJ", so morale At that time, flags shook, drums roared, the Han army advanced step by step, and the Chu army was in a mess.
Soon after the battle, the Chu army was defeated and fled.
In this story, Han Xin can quickly figure out that there are 1073 warriors, actually using a mathematical principle. According to the mathematical language, he arranged his troops three times, that is, a number divided by more than 3, more than 5, more than 3, and more than 7, to find this number.
The conditional solution of this kind of problem was first put forward by the mathematician Qin in Song Dynasty, and was called "China's remainder theorem" by later generations.
Qin is a very clever man, paying attention everywhere and learning tirelessly. Through this stage of study, he became a knowledgeable person? A versatile young scholar. When people say he is "extremely intelligent, astrology? Melody? Arithmetic, even construction. , are thoroughly studied ""game? Ball? Horse bow? The sword is unknown. "
After Qin was admitted to Jinshi, he successively served as county commandant? Pass the sentence? Senate official? National guard? Tong Nong? Temple cheng and other positions. In his spare time dealing with government affairs, he delves into mathematics and collects historical materials extensively? Math? Astrology? Melody? Establish data, such as analysis? Research.
On the occasion of his mother's death, Qin edited and sorted out his long-accumulated mathematical knowledge and research results, and wrote a world-famous masterpiece "Several Books and Nine Chapters". The book * * * lists 8 1 questions, which are divided into 9 categories, and each category has 9 questions, which not only wins in quantity, but also has top quality.
The contents of Shu Shu Jiu Zhang mainly include: great derivation, including a congruence group solution; Weather category, including calendar calculation? Precipitation; Site category, including land area; Prospecting, including Pythagoras Re-distinguish; Conscription, including losses for both sides? Taxation; Money and grain, including grain transportation? Silo volume; Architecture, including architecture? Architecture; Military competition, including camp layout? Quartermaster supply; Market items, including transactions and interest.
Shu Shu Jiu Zhang systematically summarized and developed the numerical solution and the first congruence group solution of higher-order equations, and put forward a fairly complete "three-oblique quadrature technique" and "one-skill big derivation", which reached the highest level of mathematics in the world at that time.
Qin's positive and negative balance method puts forward the principle that "quotient is always positive, real is often negative, from positive to negative, and profit is often negative", and gives a unified operation rule by pure algebraic addition, which is extended to any high-order equation.
Qin's "pros and cons" are called "Qin scheme". Countries all over the world start from primary school? When I was in middle school, I almost came into contact with his theorem in college math class? Laws and principles for solving problems.
This achievement is the highest achievement of medieval mathematics, which is five or six hundred years earlier than the same solution of Horner 18 19 in England.
Qin also improved the solution of linear equations, and eliminated them by mutual multiplication, which is completely consistent with the current addition, subtraction and elimination methods. At the same time, a rough calculation formula is given, which can be extended to the solution of general linear equations.
In Europe, it was first given by Bourdieu in 1559, more than 300 years later than Qin. Bourdieu used a very incomplete method of addition, subtraction and elimination to solve linear equations, and the theoretical integrity was not as good as Qin's.
The method of solving a kind of large-scale problems in ancient China. Qin systematically expounded the solution of this kind of problem, which is called "large extension technique", that is, the first congruence group solution in modern number theory.
This achievement is the highest achievement of medieval mathematics, which is more than 500 years earlier than the congruence theory established by the famous western mathematician Gauss in 180 1, and is called "China's remainder theorem" by the west. Qin not only won great honor for China, but also made outstanding contributions to world mathematics.
Qin also pioneered the "three-oblique quadrature method" and gave a formula for calculating the area of three sides of a known triangle. Some empirical constants are also given, such as "firm three penetrating four soil five, millet rate fifty, wall method half", which still has practical significance even now.
In Deductive Reciprocity, Qin also gave a clever and universal operation method for the mixed proposition of distribution ratio and chain ratio, which is still meaningful today.
Shu Shu Jiu Zhang is the inheritance and development of China's basic classical mathematics book Jiu Zhang Arithmetic. It summarizes the main achievements of China's traditional mathematics in Song and Yuan Dynasties, and marks the peak of China's ancient mathematics. Among them, the positive and negative cholesky decomposition and the great derivative method have long influenced the research direction of mathematics in China.
Qin's achievements represent the mainstream and the highest level of medieval mathematics development and occupy a lofty position in the history of mathematics in the world.
A famous German mathematical historian? Georg Cantor, the founder of set theory, spoke highly of the skill of "finding the solution by big deduction". He praised the China mathematician who discovered this algorithm as "the luckiest genius".
The famous American historian of science Sutton said:
Qin was one of the greatest mathematicians of his time and all times.
Triangular Zhi Ding