The development of Chinese society has different characteristics from the West, so the development of mathematics is also slightly different. In ancient China, mathematics mostly served agricultural production, and at the request of astronomy and calendar, ancient mathematics came out of an independent system different from the West. In the long history, there are many mathematicians in different fields to make outstanding contributions, today we take stock of the top 5 ancient Chinese mathematicians! Experience the path of mathematicians of different periods!
<h1>Fifth place, Jia Xian</h1>
Jia Xian (c. 11th century), an outstanding mathematician of the Northern Song Dynasty, authored the Yellow Emperor's Nine Chapters of Algorithm Fine Grass (9 volumes) and the Ancient Collection of Algorithms (2 volumes), the latter of which has been lost, and the former was copied and preserved by Yang Hui's Detailed Explanation of the Nine Chapters Algorithm. The most famous contributions are the "Jia Xian Triangle" and the "Multiplication Method".
Jia Xian triangle - the bud of binomial
This table is relatively simple to understand, that is, a trigonometric table starting from 1, and each number is the sum of the two numbers above it. Perhaps many people have not heard of "Jia Xian Triangle", but almost all of them have heard of "Yang Hui Triangle", the two of them are one thing, the reason is that Yang Hui copied Jia Xian's works. Therefore, both names can be called, and the West also calls it "Pascal Triangle".
Yang Hui Triangle (Jia Xian Triangle)
Multiplication open square - hand counting the square, worth having
There are many magic things about this table, the most famous of which is that it coincides with the coefficients of the binomial expansion. Of course, Jia Xian, who found this number table, did not know the binomial theorem, he used this triangle to open the square operation, not only to open the square, but also to open the cubic, open the fourth power and so on. And it has the advantages of simple calculation and high precision.
For example, the squared operation, x = (a + b) ² = a² + 2ab + b², when a is large, b is very small, b² can be ignored, at this time can be seen as x = a² + 2ab.
Let's take an example: for the square of 10, 10=3²+1=3²+2×3× (1/6), so we think that 10 ≈ (3+1/6) ²=3.166², and we can calculate that the square root of 10 is 3.1622776602, which shows that the accuracy of this method is still very high and super simple!
Jia Xian has a very unique insight into ancient Chinese arithmetic and is the main promoter of mathematics in the Song and Yuan dynasties!
<h1>Fourth place, Zhao Shuang</h1>
Zhao Shuang (early 3rd century), a member of the Eastern Wu dynasty at the end of the Eastern Han Dynasty. He wrote a preface to the Zhou Yi Arithmetic Sutra and made profound notes on the original text, which is the earliest commentary on the Arithmetic Sutra in China. For the first time, the proof of the Pythagorean theorem and the quadratic equation problem are given.
Zhao Shuang string diagram - "Pythagorean theorem" is illustrated and illustrated
Zhao Shuang's string diagram proves the "Pythagorean theorem" in the form of pictures and texts. The proof method is: "According to the chord diagram, it can also be multiplied by the Pythagorean as Zhu Shi TWO, multiplied by the difference of the Pythagorean strands as the middle yellow real, and the difference can be added to the real, and also become the string real." ”
Zhao Shuang string diagram
As shown in the figure, the tick is a, the strand is b, and the string is c. 2ab is the area of four right triangles, (b-a)² is the area of the middle square, and the square area is added up, that is, c². That is: (b-a) ² + 2ab = c², simplified to: a² + b² = c².
Its basic idea is the cut-and-compensate method, and the area of the figure is unchanged after cutting and compensating. The idea of cutting and supplementing has been expanded from later generations to the principle of "in-and-out complementarity". And the circumcision method is still an important method for middle school students to learn geometry!
Unary quadratic equations – not just Veda
When it comes to unary quadratic equations, it is necessary to mention the root-seeking formula, and also to mention the famous Veda theorem. And our Zhao Shuang once had a deep understanding of the univariate quadratic equation, and his conclusions were basically similar to Veda's research results, but they were not systematic and theorized, and they had no choice but to name Veda.
Zhao Shuang's mathematical ideas and methods had an important impact on the itinerary of the ancient mathematical system.
<h1>Third place, Zu Chongzhi</h1>
Zu Chongzhi (429-500), ziwen yuan. Mathematician and astronomer of the Southern and Northern Dynasties, born in Jiankang (Nanjing), mainly contributed to "Pi" and "Daming Calendar".
Pi - "Ancestral Rate"
Zu Chongzhi's "pi" was astonishingly accurate, calculating pi to 7th decimal place until the 16th century, when the Arabs broke the record. If there was a college entrance examination at that time, and if he took the mathematics test, the national champion would be Zu Chongzhi, because he was too good at calculation. However, there is no too unique innovation in the algorithm and other aspects, and the calculation method of pi still uses the "circle cutting technique" of the predecessors, but the accuracy is greatly improved, and I have to admire the computing ability of the ancestral family. His son Zu Hui is not inferior, and the father and son duo work together to calculate the volume of the ball!
"Daming Calendar" - accurate dating
In terms of computing power, the Zu family is really a model in the world, and it is not typical to talk about pi, after all, there are computers now, which have accurate pi to 31 trillion bits, compared to these 7 decimal places. But the accuracy of the "Great Ming Calendar" is simply a miracle, according to the "Great Ming Calendar" in the regression year, its length is 365.24281481 days, and the modern measurement of the length of the regression year is only six thousandths of a day, that is to say, the difference between the year is only more than 50 seconds.
Daming calendar
Modern society has telescopes, computers, Newton, Kepler, and Zu Chongzhi may only have an abacus and a pen!
<h1>Second place, Qin Jiushao</h1>
Qin Jiushao, c. 1202-1261, was a native of Qufu, Shandong, during the Southern Song Dynasty. He is the author of "Mathematical Outline", renamed "Nine Chapters of the Book of Numbers" after the Ming Dynasty, which has a total of 81 questions, including calendar calculation, precipitation calculation, area, building construction, camp layout and military supply. He is ranked second because Qin Jiushao has a world-famous algorithm called the "Chinese Surplus Theorem", also known as the "Great Yan Qiu Yi Shu". Leaving aside the content of theorem, it is extremely proud to hear the name, which is different from the "Pythagorean theorem" and "Pythagorean theorem", "Zuhui principle" and "Cavalieri principle". This theorem has only Chinese name, not english name.
China's surplus theorem - monopolizing the top of the world
The Chinese surplus theorem is also called Sun Tzu's theorem, and its problem comes from the problem of "things do not know the number" in the Sun Tzu Arithmetic Classic: "Now there are things that do not know their number, and there are three leftovers of three or three numbers; three of five and five numbers; and two left of seven or seven numbers." Q Geometry? Translated into modern mathematical language: "A number is divided by 3 by the remaining 2, divided by the remaining 3 by 5, divided by the remaining 2 by 7, to find this number?" "Although the answer 23 was given at that time, there was never a systematic solution. Until the advent of the "Great Derivative One Technique", it made a system of systems of equations with a system of simultaneous equations!
A brief introduction to the theorem:
In order to let everyone understand the theorem more bluntly, we use the problem of "things do not know the number" as an example, "a number is divided by 3 by the remaining 2, divided by 5 by the remaining 3, divided by 7 by the remaining 2, to find this number?" ", we can list a system of equations at one time: x≡2 (mod3), x≡3 (mod5), x≡2 (mod7)
We can get x=70×2+21×3+15×2, where 70 is 2 times 35, because 2×35 makes modulo 3 1. At this point, the solution is x=233, and 105 is the smallest common multiple of 3,5,7, and for 233-2× 105=23 can get the answer in the Sun Tzu Arithmetic Sutra. Through this example, I believe that everyone can understand the "Great Yan Qiu Yi Technique" very well.
The main force of the theorem is that it asserts that the system of said one-time congruence equations must have a solution, and the form of the solution is usually not important.
Chinese remainder theorem, which translates to "Chinese residual theorem", why doesn't it have an English name similar to Pythagorean theorem? Is it hard to be so generous in western mathematics? The reason for this is that our Qin Jiushao made all the Western mathematical circles shut up and put up a big thumb. Here's the thing, in the eighteenth and nineteenth centuries, Euler and Gauss gave a systematic solution to a problem of the remainder equation, and they were unaware of the existence of Mr. Qin Jiushao. In 1852, the British missionary Wei Lieali brought the solution of the "Great Yan Qiu Yi Shu" to Europe, and scholars found that the solution studied by the two great gods of Euler and Gauss was consistent with the solution of our Mr. Qin Jiushao. It is a pity that the two big mathematicians were no longer there at that time, if they knew the news, how big should the psychological shadow area be? You must know that Qin Jiushao is at least 500 years older than them!
For example, one day 500 years later, a person with his genius, independently developed a touchscreen mobile phone, and a check on the Internet found that 500 years ago there was a person named Jobs, and he had a product named IPHONE. If there were no Qin Jiushao, this theorem would have been called Euler's theorem or Gauss's theorem!
Qin Jiushao algorithm - optimization, optimization, re-optimization
Qin Jiushao algorithm should be learned by high school students, it is an optimization algorithm for polynomial evaluation. For unary n-times polynomials, when applying Qin Jiushao's algorithm for evaluation calculations, n-times addition and n-times multiplication are applied at most. To this day, the algorithm is very good, which is of great significance for improving the efficiency of computer operation and reducing CPU running time!
<h1>First place, Liu Hui</h1>
Liu Hui, c. 263 CE, was a man of the Wei and Jin dynasties, and the year of birth and death is unknown. "Young study of the "Nine Chapters", long and then detailed", the systematic annotation of the "Nine Chapters of Arithmetic", and the other "Heavy Difference" as the tenth volume of this book, perhaps Chinese still worship the number "Nine", to the Tang Dynasty "Heavy Difference" was renamed "Island Arithmetic Classic" into an independent book. Look at this height, throw out a chapter at random, it is a book!
Circumcision - naïve calculus thought.
Starting with the regular hexagon inside the circle, it is increased to 12-sided, 24-sided, 48-sided, and so on. As the saying goes, "Cut the fine, lose less." Cut and cut, so that it cannot be cut, it is integrated with the circumference, and nothing is lost. "That is, the thinner the circle is divided, the closer the area of the large rectangle is to the area of the circle." When the number of edges reaches infinity, the area of the rectangle is equal to the area of the circle, is this not the idea of limits and differentiation!
Circumcision hexagon
Circumcision is dodecagonal
Circumcision is a twenty-four-sided shape
Through the "circle cutting technique", Liu Hui obtained an approximate value of Pi accurate to the two decimal places after the decimal point of 3.14, which is the famous "emblem rate". Although this value is not as accurate as the 3.1415926 that we are familiar with, this method alone can be called a "unique skill".
In fact, our mathematicians are still too straight, if you can start again, it is recommended that Liu Huixue learn Gaussian, Gauss found the practice of the supartet, did not do it at all, just announced that I can make it, as for this specific operation who will complete? How many bits are completed? None of this sort of thing has anything to do with me. Or learn a tuition horse, record in the book, I have found a clever algorithm of pi, and can easily count a dozen, but the place is too small, I will not write.
Liu Hui's principle - infinite descending method
Liu Hui's principle is to solve the proportion problem in the volume of the cone with infinite division. To understand the principle of Liu Hui, we need to first know two animals, one called Yang Ma, one called Turtle Fang, Yang Ma is a right angle square cone, and Turtle Fang is a right angle tetrahedron, the two can be combined into a straight three prism, called graben.
The cube is divided into grabs
Yang horse with turtle calf
Liu Hui's theorem says: "One of the evil solutions is yangma and the other is turtle. Yang Ma is in the second place, turtle is in the first place, and the rate of not easy is also. It means to cut off the barrier obliquely, one is a right-angle square cone, the other is a right-angle tetrahedron, and the ratio of the volume of the square cone to the tetrahedron is 2:1.
The proof method is to divide the Yang Horse into small grabens and small Yang Horses, and the turtles into small grabs and small turtles, and these three small characters are all half of the original, and so on, until they are inseparable. It is also proved that these yang horses and turtles always meet the ratio of 2:1.
The Nine Chapters of Arithmetic Notes dominated the development of Chinese mathematics for more than 1,200 years and is a representative work of Oriental mathematics. Zu Chongzhi was famous for his circle cutting technique. Zu Hui relied on the idea of "Mou He Fang Gai" to create the Zu Hui Principle. If Archimedes is the god of Western mathematics, then Liu Hui is a well-deserved god of Eastern mathematics!