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 proofs 3 and 4, 1995 were proved by British mathematician andrew wiles.
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,
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2. Little knowledge of mathematics
This is an interesting common sense of mathematics, and it is also good to use it in mathematics newspapers.
People call 12345679 "Leak 8". This "number without 8" has many surprising characteristics, such as multiplying by multiples of 9, and the product is actually composed of the same number. People call this "uniform". For example:12345679 * 9 =1111/kloc-0. 27 = 333333333 ... 1 2345679 * 81= 999999 These are all 9 times of1multiplied by 9.
And 99, 108, 1 17 to 17 1. The final answer is:12345679 * 99 =1222212345679 *108 =13333333212345677. 444444443 ..... Paradox: (1) Russell Paradox One day, the barber in Saville Village put up a sign: All men in the village who don't cut their hair themselves will be cut by me.
So someone asked him, "Who will cut your hair?" The barber was speechless at once. 1874, the German mathematician Cantor founded the theory of * * * *, which quickly penetrated into most branches and became their foundation.
By the end of19th century, almost all mathematics was based on * * * * theory. At this time, a series of contradictory results appeared in the theory of * * *.
Especially in 1902, Russell put forward the paradox reflected in The Barber's Story, which is extremely simple and easy to understand. In this way, the foundation of mathematics has been shaken passively, which is the so-called third "mathematical crisis".
Since then, in order to overcome these paradoxes, mathematicians have done a lot of research work, produced a lot of new achievements, and brought about a revolution in mathematical concepts. (2) liar paradox: "What I said is a lie."
This paradox put forward by the Greek mathematician Euclid in the fourth century BC still puzzles mathematicians and logicians. This is the famous liar paradox.
A similar paradox first appeared in the 6th century BC, and Epimini, a Crete philosopher, once said, "All Cretes are lying." There is also a very similar sentence in China's ancient Mo Jing: "Words are contradictory, and their words are also."
It means: it is wrong to think that everything is wrong, because it is a sentence. The liar paradox takes many forms. For example, write the following two sentences on the same piece of paper: The next sentence is a lie.
The last sentence is true. What is more interesting is the following dialogue.
A said to B, "What you want to say next is' no', right? Please answer with' yes' or' no'! " This is another example. There was a devout believer who kept saying in his speech that God was omnipotent and omnipotent.
A passerby asked, "Can God make a stone that he can't lift?" 2.*** Numbers In life, we often use the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Do you know who invented these numbers? These digital symbols were first invented by ancient Indians, and then spread to * * *, and then from * * * to Europe. Europeans mistakenly think that it was invented by * * * people, so it is called "* * * number". Because it has been circulating for many years, people still call them * * *.
Now, the number * * * has become a universal digital symbol all over the world.
3. Math stories in life 100 words, 3 articles are urgent.
One Sunday morning, my parents and I watched TV at home. There was a basketball game on TV.
After watching it for a while, my father suddenly said to me, "Qiqi, let me test you a math problem to see if you can?" I opened my mouth and said, "OK, no problem." Dad thought for a moment and said, "suppose the red team throws eight balls a minute and the blue team throws six balls a minute." After eight minutes of pitching together, the blue team improved its hit rate 10 ball per minute, while the red team only threw six balls per minute because of physical exhaustion. How many minutes later, the red team and the blue team threw the same number? " I thought for a while, but it took him a long time to figure it out.
As time went by, I really couldn't think of it, so I had to say shyly, "I can't do it without a draft." I know that even if I have a draft, I may not be able to do it.
At this moment, my mother said to me: "It turns out that the red team throws two more shots a minute than the blue team, and one * * * throws eight minutes, which is 8*2= 16 (one); Later, the blue team overtook the red team and threw four more balls per minute. How many minutes does it take to throw 16 balls? 16÷4=4 (minutes), it takes 4 minutes to catch up. " I said, "It's so simple! Why didn't I think of that? " Dad smiled and said, "Is it simple? This shows that there is something wrong with your thinking.
In real life, we should be good at discovering things and finding out their laws, then you will feel that mathematics in life is much more interesting than that in class. Through this incident, I found that mathematics in life is indeed everywhere, everywhere in life and study.
From then on, I like math more! Comments (2)3 148 Other answers (2) An enthusiastic friend, animal mathematical meteorologist Lorenz, published a paper entitled "Will butterflies flap their wings to cause tornadoes in taxonomic groups?" This paper discusses that if the initial condition of a system is a little worse, its result will be very unstable. He called this phenomenon "the butterfly effect". Just like we roll the dice twice, no matter how deliberately we roll, the physical phenomena and points thrown twice are not necessarily the same.
Why did Lorenz write this paper? This story happened in the winter of 196 1 2008. He operated the meteorological computer in the office as usual. Usually, he only needs to input meteorological data such as temperature, humidity and air pressure, and the computer will calculate the possible meteorological data at the next moment according to the built-in three differential equations, thus simulating the meteorological change map.
On this day, Lorenz wanted to know more about the subsequent changes of a record. He re-entered the meteorological data at a certain moment into the computer, so that the computer could calculate more subsequent results. At that time, the speed of computer processing data was not fast enough, so he had time to have a cup of coffee and chat with his friends for a while before the results came out.
An hour later, the result came out, but he was dumbfounded. Compared with the original information, the original data is similar, and the later data is more different, just like two different pieces of information.
The problem is not the computer, but the data he entered is 0.0005438+027. These subtle differences make a world of difference. So it is impossible to accurately predict the weather for a long time.