Everyone knows that we have been studying mathematics since primary school. Do you know the development history of some mathematics? The following picture of the math handwritten newspaper I carefully arranged for you is simple and beautiful. Welcome to read!

The design of mathematical handwritten newspaper is concise and beautiful.

Mathematical manuscript design 1

Content of Mathematical Manuscripts: Development of Ancient Mathematics in China

Metaphysics, which appeared in Wei and Jin dynasties, was not bound by Confucian classics in Han dynasty and was active in thought. It can argue and win, use logical thinking and analyze truth, all of which are conducive to improving mathematics theoretically. During this period, the Nine Chapters Heavy Difference Diagram appeared in Wu and Zhao's annotation of Zhou Huishu, Xu Yue's annotation of Nine Chapters Arithmetic in the late Han Dynasty and early Wei Dynasty, and Liu Hui's annotation of Nine Chapters Arithmetic in the Wei and Jin Dynasties. The work of Zhao Shuang and Liu Hui laid a theoretical foundation for the ancient mathematical system of China.

Zhao Shuang was one of the earliest mathematicians who proved and deduced mathematical theorems and formulas in ancient China. He added this sentence in the book "Week Fast Shu Jing"? Pythagoras and notes? And then what? Daily height map and notes? This is a very important mathematical document. Are you online? Pythagoras and notes? He put forward five formulas to prove Pythagorean theorem, and solved Pythagorean form with string diagram 2. Are you online? Daily height map and notes? Zhao Shuang's work is groundbreaking and plays an important role in the development of ancient mathematics in China.

Liu Jicheng, who was contemporary with Zhao Shuang, developed the thought of the famous Mohist in the Warring States Period, and advocated strict definition of some mathematical terms, especially important mathematical concepts, and thought that mathematical knowledge must be carried out? Dissociation? In order to make mathematical works concise, close and beneficial to readers. His Notes on Nine Chapters of Arithmetic not only explains and deduces the methods, formulas and theorems of nine chapters of arithmetic as a whole, but also gets great development during the discussion. Liu Hui created secant, proved the formula of circle area by using the idea of limit, and calculated the pi as 157/50 and 3927/ 1250 by theoretical method for the first time.

Liu Hui proved by infinite division that the volume ratio of right-angled square cone to right-angled tetrahedron is always 2: 1, which solved the key problem of general solid volume. When proving the volume of square cone, cylinder, cone and frustum, Liu Hui put forward the correct method to solve the volume of sphere completely.

After the Eastern Jin Dynasty, China was in a state of war and north-south division for a long time. The work of Zu Chongzhi and his son is the representative work of the development of mathematics in South China after the economic and cultural shift to the south. On the basis of Liu Hui's Notes on Nine Chapters of Arithmetic, they greatly promoted traditional mathematics. Their mathematical work mainly includes: calculating pi between 3.1415926 ~ 3.1415927; Put forward the principle of ancestral pestle; The solutions of quadratic and cubic equations are put forward.

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Presumably, Zu Chongzhi calculated the inscribed area of regular polygon 6 144 and regular polygon 12288 on the basis of Liu Hui secant method, and obtained this result. He also obtained two fractional values of pi by a new method, namely the approximate ratio of 22/7 and the density ratio of 355/ 1 13. Zu Chongzhi's work made China lead the west in the calculation of pi for about one thousand years.

Zu Chongzhi Zi Zuxuan summed up Liu Hui's related work and put forward? If the power supply potential is the same, the products cannot be different? That is, two solids with the same height, if the horizontal cross-sectional area of any height is equal, the volumes of the two solids are equal, which is the famous axiom of ancestors. Zu Xuan applied this axiom to solve Liu Hui's unsolved spherical volume formula.

Emperor Yang Di was overjoyed and made great achievements, which objectively promoted the development of mathematics. In the early Tang Dynasty, Wang Xiaoyu's "Jigu Shujing" mainly discussed earthwork calculation, division of labor, acceptance and calculation of warehouses and cellars in civil engineering, which reflected the mathematical situation in this period. Wang Xiaotong established the cubic equation of number without using mathematical symbols, which not only solved the needs of the society at that time, but also laid the foundation for the establishment of the art of heaven. In addition, for the traditional Pythagorean solution, Wang Xiaotong also used the digital cubic equation to solve it.

In the early Tang Dynasty, the feudal rulers inherited the Sui system, and in 656, they set up the Arithmetic Museum in imperial academy, with 30 students, including arithmetic doctors and teaching assistants. Ten arithmetic classics edited and annotated by Taishiling Li are used as teaching materials for students in the Arithmetic Museum and as the basis for verifying arithmetic. Ten Books of Calculating Classics compiled by Li and others is of great significance in preserving classical works of mathematics and providing literature for mathematical research. Their notes on Zhoupian suan Jing, Nine Chapters Arithmetic and Island Suan Jing are helpful to readers. During the Sui and Tang Dynasties, due to the need of calendar, celestial mathematicians created quadratic function interpolation method, which enriched the content of ancient mathematics in China.

Calculation and compilation was one of the main calculation tools in ancient China. It has many advantages, such as simplicity, image and concreteness, but it also has some disadvantages, such as large compiling area and easy to make mistakes when the operation speed is accelerated. So the reform was carried out very early. Among them, Taiyi, Ermi, Sancai and Abacus are all abacus with beads, which is an important technical reform. Especially? Abacus? , inherits the advantages of calculating the sum of five liters of decimals, overcomes the shortcomings of calculating vertical and horizontal notation and the inconvenience of arranging chips, and has obvious advantages. But at that time, the multiplication and division algorithm could not be performed continuously. The abacus beads have not been worn and are not easy to carry, so they are still not widely used.

1? The magical use of.

There are eight cups on the table, all with their mouths up. Turn four cups at a time. Just turn them twice and they will all come down. If you change the eight cups in the question into six cups, and still turn four cups at a time, can you turn them all down after a few somersaults?

Please try it. At this time, you will find that you can achieve your goal by turning three somersaults. The explanation is as follows:

With+1, the cup mouth is up,-1, and the cup mouth is down. These three flipping processes can be simply expressed as follows:

Initial state:+1,+1,+1,+1.

First flip:-1,-1,-1,-1,+1.

Second flip:-1,+1,+1,+1,-1,+L.

The third flip:-1,-1,-1,-1.

If you change the 8 blocks in the question into 7 blocks, can you turn them all down several times (4 blocks at a time)?

After several experiments, you will find that you can't refuse them all.

Is it yours? Flip? Poor ability, or can't you finish it at all?

1? I'll tell you, no matter how many times you turn it over, you can't let these seven cups face down.

There is a simple reason. +1 means that the cup mouth is up,-1 means that the cup mouth is down, and the question becomes:? Change the symbols of 4 of 7+1 at a time, and whether they can all become-1 after several times. Considering the product of these seven numbers, because the sign of the four numbers changes every time, their product will never change (that is, it will always be+1), but in the case of all cups falling down, the product of seven numbers cannot be equal to-1.

The reason is so simple and the proof is so clever, thanks to 1? Language.

In China's chess, the horse goes to the sun. Did you find the following phenomena during the game?

When a horse jumps from a certain position, it must go through even steps to return to its original position.

1? Language can also help you prove this result:

? There are nine chessboards? 10=90 positions, and adjacent positions are represented by numbers with different symbols (+and-1) (all solid point positions in the figure are represented by+1, and the rest are represented by-1), then the sign of the chess horse will change every step from any position. In other words, the chess horse will change its symbol.

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