Interesting knowledge of mathematics

Number theory part:

1, there is no maximum prime number. Euclid gave a beautiful and simple proof.

2. Goldbach conjecture: Any even number can be expressed as the sum of two prime numbers. Chen Jingrun's achievement is that any even number can be expressed as the sum of the products of one prime number and no more than two prime numbers.

3. Fermat's last theorem: n power of x+n power of y = n power of z, and n> has no integer solution at 2 places. Euler proved that 3 and 4, 1995 was written by a British mathematician.

Andrew Wiles

certificate

Topology part:

1. The relationship among points, faces and edges of a polyhedron: fixed point+number of faces = number of edges +2, which was proposed by Descartes and proved by Euler, also known as euler theorem.

2. euler theorem's inference: There may be only five regular polyhedrons, namely regular tetrahedron, regular octahedron, regular hexahedron, regular icosahedron and regular dodecahedron.

3. Turn the space upside down, the left-handed object can be changed into the right-handed, and through Klein bottle simulation, a good mental gymnastics,

Excerpted from: /bbs2/ThreadDetailx? id=3 1900

2. Interesting little knowledge

Little knowledge, physical interest-the "weight of things" that will change. After learning the relevant physical knowledge, students may know that the weight of the object itself is not static, that is, it is sometimes "weightless"; Sometimes it is "overweight".

What causes the change in the weight of an object? Don't worry, let's look at the following story first: Once upon a time, there was a story: a businessman bought 5000 tons of herring from Dutch fishermen, loaded it on a boat and transported it from a Dutch city to the seaport of Maga, an African city near the equator. When I got there, I weighed it and found that the herring was nearly 19 tons short.

Strange! Where did it go? It can't be stolen because the ship didn't call all the way. At that time, no one could reveal the secret, but now we finally know the reason: it turned out that this was a joke played by gravity.

Because the earth is slightly oval, its radius of north and south poles is 20 kilometers smaller than that of equator. The smaller the radius, the greater the attraction; or vice versa, Dallas to the auditorium

Therefore, when the Dutch 5000 tons of herring are transported near the equator, the weight of herring naturally becomes "light". In addition, the weight of the object changes a lot! If you are on a high mountain, it is lighter than on the flat ground; The equator is lighter than the poles; It is much lighter in water than on land, and so on.

As you can imagine, if you fly to a high altitude area where the gravity of the earth can't reach, there is no weight at all, because the gravity of the earth is very small. However, no matter how it changes, the quality of the object will not change! Well, now everyone knows the truth! In fact, there are many similar problems around us. As long as we can find it in time and combine it with theory, we can find the correct answer.

I believe that if you encounter similar problems in the future, don't be "helpless"! A cat has 230 bones. Cats are more sensitive to hearing than people and dogs.

Compared with its size, cats have bigger eyes than any mammal. The normal pulse of a cat is between 1 10 and 170 beats per minute.

The normal temperature of a cat is about 39 degrees. The vertical jumping height of a cat can reach five times its own height.

A cat's nose print is unique. No two cats have the same nose print. Cats react more strongly to women than men because women's voices are more frequent than men's.

The running speed of domestic cats is about 55 to 60 kilometers per hour. Cats are the most sleepy mammals, sleeping about 16 hours a day.

Birds are interesting and have little knowledge. What bird is not easily noticed? When you pass a tree with a woodcock in the forest, you may not notice that there is a woodcock in the tree. The woodcock is not a very small bird, but a big bird, but its beautiful feathers look like fallen leaves in autumn, so it is not easy to be noticed because it pretends to be motionless. The woodcock stands in the tree, always paying attention to the surrounding situation, even if there is a little movement behind him, it can immediately detect it.

This is because its eyes are located at the back of its head, so no enemy can escape its sight. Of course, few insects can escape it.

Where does grouse live? Grogrouse lives in the cold zone of the northern and southern hemispheres and is one of the few birds in the cold zone. In winter, birds perch on pine or fir trees.

In order to resist the cold climate, it must eat a lot of needles to generate energy. Near the polar regions, the days are short and the nights are long in winter, so grouse eat almost all day.

Spring has come, and grouse have started courtship. They usually choose the male bird by the female bird, and they must win the competition to win the favor of the female bird.

Do parrots chat with each other? "Baby, get up!" Some parrots can talk, but they don't really talk. Parrots' owners patiently teach them to say some simple words. Although they can read them, they don't understand the meaning at all.

Animals can communicate with each other in their own way, not in the language we understand. Their crying may mean: "I'm afraid"; "Please touch me"; "I found food" or "danger! Run! " Colors, movements and smells can also be used as communication tools between animals.

Hunters can set traps by imitating their sounds and smells, and let them trap themselves. Penguins can't build nests? In fact, penguins can't build nests.

When the mother penguin went to the sea to look for food, the father penguin stood on the land, put the egg between his feet, covered the egg with a fat belly, and hatched the egg. Penguins hatch their eggs in the same place every year. They use their beaks and wings to deal with possible enemies and protect their offspring.

Newborn penguins will look for food in their parents' mouths. Penguins feed on fish, shrimp and shells.

In the summer when food is abundant, they spend all their time supplementing nutrition, and can usually dive into the sea hundreds of meters deep to find food. Can Penguin Fly Penguin is a very strange animal, dull but cute.

Their feet are like wearing the same trouser legs, and it is very difficult to walk. Penguins always contract their wings to keep their balance.

Although they can't fly, they still belong to birds. Their heavy clothes are covered with very tight little feathers, which are all covered with oil.

Penguins flap their wings in the water as if equipped with an engine. Penguins are very lively and like diving and playing in the water very much.

When they avoid natural enemies, they often surface and can glide in the air 1 m or more. What kind of nest is the most beautiful? There are many kinds of birds flying in the sky, and each bird has a different nest.

Hummingbirds' nests are smaller than spoons, and some eagles' nests are bigger than cars. Birds use fluff, branches, saliva or cobwebs as nesting materials.

The shape of the bird's nest, some like bowls, some like balls; Some hang like cradles, others float on the water like rafts. There are hundreds of species of weaver birds in Africa, and their nests are very complicated. Some birds also paint their nests to attract the attention of females.

There are many kinds of bird's nest in the world, which one is the most beautiful! How do birds fly long distances? Birds fly in groups for days on a long journey. For example, terns fly from the North Pole to the South Pole in this way, which is about 20 thousand kilometers away.

The long flight of birds is actually very hard. Fly.

3. 10 Mathematical Story (shortest)

Where is the one yuan?

Three people stayed in a hotel, and the price per person per day was 10 yuan. Everyone paid 10 yuan, and the total was the boss 30 yuan. Later, the boss gave a discount of 5 yuan and asked the waiter to return it to them. As a result, the waiter embezzled 2 yuan, and each of the remaining 3 yuan returned 1 yuan, which means that each person spent 9 yuan's money. Three people spent a total of * * * 27 yuan, plus 2 yuan, a corrupt waiter, spent a total of * * * 29 yuan. Where did the dollar go?

Divide apples

There are five students in Xiaomi's family Xiaomi's father wants to entertain six children with apples, but there are only five apples at home. What shall we do? I have to cut the apple, but I can't cut it into pieces. Xiaomi's father wants each apple to be cut into three pieces at most. This has become another topic: divide five apples equally among six children, and each apple is not allowed to be cut into more than three pieces.

How did Xiaomi's father do it?

Ma Xiao Hu cooked chicken

During the Spring Festival, Xiao Mahu, a professional chicken farmer, stood in the yard, counted the total number of chickens, decided to stay and gave 1/2 to the nursing home. After he sent the chickens away, he heard the chickens crowing in the room, only to know that there were 10 chickens missing. So I counted the chickens inside and outside the room again, and there was nothing wrong, no more, no less, just 1/2 left. Little careless and strange. What's the problem? Do you know how many chickens Xiao Mahu counted in the yard? "This article is organized by the first model essay network, and the copyright belongs to the original author and the original source. 』

How many guests came one day and Xiao Lin was washing dishes at home. Xiao Qiang saw it and asked, "Why do you wash so many bowls?" "

We have guests at home. ""How many people came? " Kobayashi said, "I don't know. I only know that each of them uses a rice bowl, two people share a soup bowl, three people share a vegetable bowl, four people share a big wine bowl, and one * * uses 15 bowl. "Do you know how many guests are here?

4. What are the interesting tricks of China national flag?

The red flag symbolizes the revolution. There are five yellow five-pointed stars on the upper left; One star is larger and ranks to the left; All four stars are relatively small, arching to the right of the big star, and each star has a sharp angle facing the center of the big star.

Notes to the National Flag Law of People's Republic of China (PRC):

Description of the method of making the national flag, article 3 of which stipulates:

(3) The general standards of the national flag are as follows:

A, length 288 cm, height 192 cm.

B: It is 240 cm long and 160 cm high.

C, length 192 cm, height 128 cm.

Ding, length 144 cm, height 96 cm.

E, 96 cm long and 64 cm high.

Full text of the national flag making method:

Instructions on how to make the national flag

(Promulgated by the Presidium of the First Plenary Session of China People's Political Consultative Conference, September 28, 2004, 1949)

The shape and color of the national flag are the same, but the five stars on the national flag are opposite. For convenience, this film only takes the left flagpole as the description standard. If the flagpole is on the right side, the left side in this document should be changed to the right side, and the right side should be changed to the left side.

(1) The flag surface is a red rectangle with a length and width of three to two, and there are five yellow five-pointed stars on the upper left of the flag surface. A star is larger, and its circumscribed circle diameter is three-tenths of the height of the flag, ranking on the left; The four stars are smaller, the diameter of the circumscribed circle is one tenth of the height of the flag, and the ring arch is on the right side of the big star. The flagpole cover is white.

(2) The position and drawing of the five stars are as follows:

A. To determine the position of the five stars, first divide the flag surface into four equal rectangles, divide the rectangle in the upper left corner into ten equal parts from top to bottom, and divide it into fifteen equal parts from left to right.

B, the center of the big five-pointed star, five times five, five left and ten right in the rectangle. Its drawing method is: take this point as the center and make a circle with the radius of three divisions. On this circumference, five equidistant points are determined, one of which must be directly above the circle. Then connect the two points separated by these five points to make them into a straight line. The outer contour formed by these five straight lines is the required five-pointed star. One corner of the five-pointed star is facing up.

C. The center points of four small five-pointed stars, the first point is on the rectangle, the second point is on the rectangle, the third point is on the rectangle, the third point is on the rectangle, and the fourth point is on the rectangle. Its drawing method is: take the above four points as the center and divide them into four circles with equal radius. Set five equidistant points on each circle, one of which must be located on the connecting line between the center of the five-pointed star and each of the above four centers. Then use the same method to form a big pentagram and a small pentagram. Four small pentagrams, each with an angle pointing directly to the center of the big pentagram.

(3) The general standards of the national flag are as follows:

A, length 288 cm, height 192 cm.

B: It is 240 cm long and 160 cm high.

C, length 192 cm, height 128 cm.

Ding, length 144 cm, height 96 cm.

E, 96 cm long and 64 cm high.

2:

Instructions on how to make the national flag

(Promulgated by the Presidium of the First Plenary Session of China People's Political Consultative Conference, September 28, 2004, 1949)

The shape and color of the national flag are the same, but the five stars on the national flag are opposite. For convenience, this film only takes the left flagpole as the description standard. If the flagpole is on the right side, the left side in this document should be changed to the right side, and the right side should be changed to the left side.

(1) The flag surface is a red rectangle with a length and width of three to two, and there are five yellow five-pointed stars on the upper left of the flag surface. A star is larger, and its circumscribed circle diameter is three-tenths of the height of the flag, ranking on the left; The four stars are smaller, the diameter of the circumscribed circle is one tenth of the height of the flag, and the ring arch is on the right side of the big star. The flagpole cover is white.

(2) The position and drawing of the five stars are as follows:

A. To determine the position of the five stars, first divide the flag surface into four equal rectangles, divide the rectangle in the upper left corner into ten equal parts from top to bottom, and divide it into fifteen equal parts from left to right.

B, the center of the big five-pointed star, five times five, five left and ten right in the rectangle. Its drawing method is: take this point as the center and make a circle with the radius of three divisions. On this circumference, five equidistant points are determined, one of which must be directly above the circle. Then connect the two points separated by these five points to make them into a straight line. The outer contour formed by these five straight lines is the required five-pointed star. One corner of the five-pointed star is facing up.

C the center points of the four small five-pointed stars, the first point is on the rectangle, the second point is on the rectangle, the third point is on the rectangle, the third point is on the rectangle, and the fourth point is on the rectangle. Its drawing method is: take the above four points as the center and divide them into four circles with equal radius. Set five equidistant points on each circle, one of which must be located on the connecting line between the center of the five-pointed star and each of the above four centers. Then use the same method to form a big pentagram and a small pentagram. Four small pentagrams, each with an angle pointing directly to the center of the big pentagram.

5. Mathematics is more interesting, and the short knowledge is about 20 to 50 words.

Interesting mathematical knowledge number theory part: 1, there is no maximum prime number.

Euclid gave a beautiful and simple proof. 2. Goldbach conjecture: Any even number can be expressed as the sum of two prime numbers.

Chen Jingrun's achievement is that any even number can be expressed as the sum of the products of one prime number and no more than two prime numbers. 3. Fermat's last theorem: n power of x+n power of y = n power of z, and n> has no integer solution at 2 places.

Euler proofs 3 and 4, 1995 were proved by British mathematician andrew wiles. Topology part: 1, the relationship between points and edges of polyhedron: fixed point+number of faces = number of edges +2, which was proposed by Descartes and proved by Euler, also known as euler theorem.

2. euler theorem's inference: There may be only five regular polyhedrons, namely regular tetrahedron, regular octahedron, regular hexahedron, regular icosahedron and regular dodecahedron. 3. Turn the space upside down, and the left-handed object can become the right-handed one. Through Klein bottle simulation, a good brain gymnastics is extracted from: /bbs2/ThreadDetailx? id=3 1900 .

6. Interesting knowledge about cherishing time

Cherish time 1

Lu Ji said in "Short Songs": "What is the geometry of life? Die like a sunrise. Without weight, China is not in the sun. " Life is just a few autumn, and it is also a flick of a finger. No matter what you do, cherish time. Don't sigh that life is short and let time pass by you in vain.

Zhuangzi said: "If there is a gap between heaven and earth in life, it is sudden." The first kind of people just think that a short life, if you don't eat, drink and be merry in time, isn't it a waste? They hold the attitude of "there is wine today, we will be drunk tomorrow, and I will sing and laugh like a dream" and spend all their time playing, like parasites. The second kind of people know that "it is difficult to wake up in the morning before the prime of life", so they feel the pain of "time waits for no one" and immerse themselves in work and study all day, so that every minute of their lives can be enriched and shine, which also reflects Edison's words: "Life is short, there are too many things to do, and I have to race against time."

Of course, time will only give these two different results: first, doing nothing all day, leaving only endless regrets; Secondly, efforts have brought fruitful results. With their diligence and wisdom, they have made great contributions to the country, and the society has affirmed their life value, and they are proud of it.

At this point, who can say that time is not a great wealth? Cherishing time will make you the master of time; Cherishing time will enrich your life.

Zhu Ziqing once said in the article "Hurry": "When washing your hands, the days pass from the basin; When eating, the days pass from the rice bowl. When you think it has left in a hurry, when you reach out to cover it, it passes through the blocked fingers again. When it is dark, when you lie in bed, it will jump over you and fly away from your feet. "

Mr. Lu Xun once said: "Saving time means making your life more effective, that is, prolonging your life."

Cherish time 2

"Tomorrow after tomorrow, how many tomorrows, I can't live tomorrow, and everything is in vain! If the world is tired of tomorrow, it will go to Qiu Lai to watch the flowing water in spring and the sunset at dusk. How can it be tomorrow after a hundred years? "

This song tells a story of looking forward to tomorrow and letting today pass. Listening to the faint cry of Hao Han birds, it sounded in the severe winter: "The cold wind froze me to death, and I will build a nest tomorrow."

The autumn wind is bleak, winter is coming, and the birds in Hao Han are frozen stiff, so they say, "The cold wind will freeze me to death, and I will build a nest tomorrow." It's dawn Look at the warm sunshine. Enjoy it first. Let's start nesting tomorrow. It's night again.

The cold wind froze me to death, and I will build a nest tomorrow. Hao Han bird began to crow again, but the next day, it saw the sun smiling and stopped. . As the days passed, the Hao Han bird never fulfilled its promise, still flapping its wings in the cold wind and singing "The cold wind froze me to death, and I will build a nest tomorrow". Winter is coming soon. Hao Han bird has been frozen to death, but its mouth is still vaguely shouting "cold … wind … freezing … kill me, tomorrow …".

Yes! Time is the fairest judge. Whether you are rich or poor, you will be fairly allocated excellent time, 365 days a year, 24 hours a day, 86,400 seconds, no more, no less, depending on how you arrange it reasonably. Maybe someone will create a great invention or explore a new element in one day, or maybe someone will do nothing and waste time in one day. So how can we cherish time? Then you should be diligent, don't let the day go by, do something useful every moment, and quit some unnecessary actions, so that you will become the master of time and time will smile at you.

Let's not fantasize about tomorrow or lament yesterday. What we should cherish most is "today", a real world. As Mr. Wen Jia said: "Today is today, today is rare, so we won't do it today. When is this? Life is a hundred years today, today is not a pity! If you wait until tomorrow, something will happen in the Ming Dynasty, so please start today.

We are all flowers of the motherland, so we should join hands and cherish time. Let's cherish time and be the master of it!

Cherish time 3

Time is life, Mr. Lu Xun said: "wasting your own time is equal to chronic suicide, and wasting others' time is equal to killing people for money." "This shows the importance of cherishing time.

Scholar's time: "an inch of time is worth an inch of gold, and an inch of gold can't buy an inch of time." Only by cherishing time can scholars create their own value and open up new knowledge fields for the development of human civilization. Science and technology can further develop and contribute their talents to the soaring of the motherland. On the other hand, if you don't cherish time, you will not only ruin your future, but also bring economic losses to the country.

For military scientists, cherishing time is victory. The Red Army will fly over the Jinsha River and March day and night in order to gain time and win. This shows how important it is to cherish time, which is related to the life and death of the motherland.

For economists, time is money and efficiency. With the tide of reform and opening up, people pay more and more attention to time. In the past, people were slack in their work and ate the same pot less and less. What is presented now is to seize the time to create benefits and wealth.

Cherishing time means cherishing life. Life is very important to everyone. We should cherish time and create our own life value.