Liu Hui's life is a life of hard exploration of mathematics. He is not a mediocre man who seeks fame and fame, but a great man who never tires of learning. He left us a valuable fortune.
Liu Hui, an outstanding mathematician in Wei and Jin Dynasties, once put forward a plan to measure the height of the sun:
In the open space outside Luoyang, one pole is 8 feet long, one pole is in the south and the other pole is in the north. At noon that day, measure the projection of the sun to these two poles, take the difference of shadow length as the denominator, multiply the length of the pole by the distance between the two poles as the numerator, and divide the two poles to get the vertical height of the sun to the surface.
Multiply the shadow length of the South Pole by the distance between the two poles as molecules, and then divide by the difference of the shadow length to get the distance from the South Pole to directly below the sun.
Taking these two numbers as the side lengths of two right-angled sides of a right-angled triangle, the chord length of the right-angled triangle is calculated by Pythagorean theorem, and the actual distance from the sun to the observer is obtained.
Liu Hui's scheme applies the growth ratio principle of corresponding line segments in similar triangles, and skillfully connects two other seemingly unrelated triangles with a middle triangle.
All this is exactly the same as what we learned in the plane geometry textbook of middle school today. If the sun in the Liu Hui problem is replaced by another light source, it will be no problem at all if it is designed as geometric proof questions and calculation questions and put into today's middle school textbooks.
Liu Hui's mathematical works are rarely handed down to later generations, and all of them have been copied over and over again. His main works are: Nine Chapters of Arithmetic Notes (volume 10); The weight difference (1) was renamed as island calculation in the Tang Dynasty.
Liu Hui's ability to write Nine Chapters of Arithmetic Notes is related to his life background.
The turmoil at the end of the Han Dynasty broke the dogmatic situation of Confucian classics in the Western Han Dynasty, and the thought was liberated. Although there was no great unity, there was a brief period of relative unity and ideological emancipation? The situation of academic contention.
In addition, at the end of the Eastern Han Dynasty, Buddhism entered China, Taoism began to rise, and Confucianism and Taoism began to merge. Some people began to explain Confucian things with Taoist thought. A hundred schools of thought contend? Discrimination and understanding promoted the logical thinking of China people at that time.
The logic problem that has been abolished or stopped for many years has been raised in academic circles again.
Because mathematics is a logical process, there is logical reasoning? Logic proves that mathematics is unimaginable without such things as the foundation. The recovery and development of science and technology need some scientific and technological things to promote the development of productive forces. Therefore, Liu Hui's mathematical thought came into being under this background.
In fact, he was the first person in China who explicitly advocated using logical reasoning to demonstrate mathematical propositions.
Judging from Nine Chapters Arithmetic itself, it was written in the early years of the Eastern Han Dynasty, and there are 246 ways to solve problems. In many aspects, such as solving simultaneous equations, calculating four fractions, calculating positive and negative numbers, calculating the volume and area of geometric figures, etc. , all belong to the advanced ranks in the world.
However, due to the primitive solution in the original book and the lack of necessary proof, Liu Huize wrote "Nine Chapters of Arithmetic Notes" and made supplementary proof. These proofs show his creative contributions in many aspects.
The Book of Archipelago Calculations was originally the continuation and development of Pythagoras, the ninth volume of Nine Chapters Arithmetic Note, and was called Nine Chapters Heavy Difference Map, which was attached to Nine Chapters Arithmetic Note as the tenth chapter. In the Tang dynasty, it was separated from it and became a book alone. According to the first topic "Today's Island of Hope", it is named "Island Calculation Classic", which is one of the ten books of calculation classics.
The research objects in Island Calculation are all about the measurement of height and distance, and the tools used are all measuring rods and horizontal rods connected vertically.
All problems are calculated by using data obtained from two or more observations. It is the earliest work of surveying mathematics in China, and it also provides a mathematical basis for cartography.
Is "Island Computing" used twice? Three times? The fourth observation method is a leading creation in the history of measurement. Scholars at home and abroad spoke highly of the achievements of the Book of Island Calculations.
American mathematician Frank Schwaetzer said:
China's geodesy reached its peak with "island calculation", and China's achievements in mathematical geodesy surpassed those of the west by about 1000 years.
Liu Hui's mathematical achievements can be roughly summarized into two aspects: one is to clean up China's ancient mathematical system and lay its theoretical foundation; Second, on the basis of inheritance, put forward your own ideas.
Liu Hui's achievements in the ancient mathematical system are embodied in Notes on Arithmetic in Nine Chapters. In fact, this book has formed a relatively complete theoretical system.
In Number Theory, Liu Hui expounded the general score with the same number and different number. About integrals? Four operations, and the algorithm of simplifying complex numbers; In the annotation of prescription, he discussed the existence of irrational roots from the infinite meaning of prescription, introduced new numbers, and created a method of infinitely approaching irrational roots with decimals.
In putting forward calculus theory, Liu Huixian gave a clear definition of rate, and also used multiplication? A contract? On the basis of homogeneous basic operation, the unified theoretical basis of number and expression operation is established. He also used "rate" to define "equation" in China's ancient mathematics, that is, the augmented matrix of linear equations in modern mathematics.
In the aspect of Pythagorean theory, Liu Hui demonstrated Pythagorean theorem and the calculation principle of solving Pythagorean shape one by one by analyzing typical figures such as "horizontal in the hook" and "straight in the strand", established the theory of similar Pythagorean shape, developed Pythagorean measurement, and formed a similar theory with China characteristics.
In the theory of area and volume, Liu Hui supplemented it with differences. Liu Hui's principle is based on the principle of making up the loss by profit and the "secant" limit method, and various geometric shapes are solved. The area of the geometry? Volume calculation problem. The theoretical value of these aspects is still shining.
Liu Hui's work not only had a far-reaching impact on the development of ancient mathematics in China, but also laid a lofty historical position in the history of mathematics in the world. In view of Liu Hui's great contribution, many books call him "Newton in the history of Chinese mathematics".
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