A little knowledge of mathematical culture (about mathematics)

1. A little knowledge about mathematics

1, zero

At a very early time, people thought that "1" was the beginning of "numerical character table", which further led to other numbers such as 2, 3, 4 and 5. The function of these figures is to count those physical objects, such as apples, bananas and pears. Only later, when there were no apples in the box, did I learn how to count the apples in the box.

2. Digital system

Digital system is a way to deal with "how much". Different cultures have adopted different methods in different times, from the basic "1, 2,3, many" to the highly complex decimal notation used today.

3,π

π is the most famous number in mathematics. Forget all other constants in nature, and you won't forget them. π always appears at the first place in the list. If the number also has an Oscar, then π will definitely win the prize every year.

π or π is the ratio of the circumference of a circle to its diameter. Its value, that is, the ratio of these two lengths, does not depend on the size of the circumference. Whether the circumference is large or small, the value of π is constant. π comes from the circumference, but it is everywhere in mathematics, even involving those places that have nothing to do with the circumference.

4. Algebra

Algebra gives a brand-new method of solving problems, a "cyclotron" method of playing with years. This kind of "maneuver" is "reverse thinking". Let's consider this problem. When the number 25 is added with 17, the result is 42. This is a positive idea. All you need to do is add up these figures.

However, if you already know the answer 42 and ask a different question, what you want to know now is what number and 25 add up to 42. You need to use reverse thinking here. To know the value of unknown x, satisfy equation 25+x=42, and then subtract 25 from 42 to know the answer.

5. Function

Leonhard euler is a Swiss mathematician and physicist. Euler was the first person to use the word "function" to describe expressions containing various parameters, such as: y? =? F(x), one of the pioneers who applied calculus to physics.

2. Math tips

Goldbach conjecture About 250 years ago, the German mathematician Goldbach discovered that any integer greater than 5 can be expressed as the sum of three prime numbers.

He verified many figures, and this conclusion is correct. But he couldn't find any method to prove it completely in theory, so he wrote a letter on June 7, 742/kloc-0, asking Euler, a famous mathematician who worked at the Berlin Academy of Sciences at that time.

Euler seriously thought about this problem. He first looked up a long numerical table one by one: 6 = 2+2+2 = 3+38 = 2+3+3 = 3+59 = 3+3+3 = 2+710 = 2+3+5 = 5+51/kloc. 38+07+7 1=97+3 10 1=97+2+2 102=97+2+3=97+5 …… 。

Extended Goldbach conjecture About 250 years ago, German mathematician Goldbach discovered a phenomenon that any integer greater than 5 can be expressed as the sum of three prime numbers. He verified many figures, and this conclusion is correct.

But he couldn't find any method to prove it completely in theory, so he wrote a letter on June 7, 742/kloc-0, asking Euler, a famous mathematician who worked at the Berlin Academy of Sciences at that time. Euler seriously thought about this problem.

He first looked up a long numerical table one by one: 6 = 2+2+2 = 3+38 = 2+3+3 = 3+59 = 3+3+3 = 2+710 = 2+3+5 = 5+51/kloc. 38+07+71= 97+310/= 97+2102 = 97+2+3 = 97+5 ... This table can be expanded infinitely, and every expansion increases Euler's confidence in affirming Goldbach's conjecture. And he found that the problem of proof should actually be divided into two parts.

That is, it is proved that all even numbers greater than 2 can always be written as the sum of two prime numbers, and all odd numbers greater than 7 can always be written as the sum of three prime numbers. When he finally believed that this conclusion was true, he wrote back to Goldbach on June 30th.

The letter said: "Any even number greater than 2 is the sum of two prime numbers. Although I can't prove it yet, I am sure it is completely correct. " Because Euler is a famous mathematician and scientist, his self-confidence has attracted and inspired countless scientists to try to prove it, but there was still no progress until the end of 19. This seemingly simple but extremely difficult problem of number theory has long plagued the mathematics community.

Whoever can prove it can climb a lofty and strange mountain in the kingdom of mathematics. So some people compare it to "a pearl in the crown of mathematics".

In fact, a large number of numbers have been verified, and the verification of even numbers has reached more than 6543.8+0.3 billion, and no counterexample has been found. So why can't this question be concluded? This is because there are infinitely many natural numbers, and no matter how many numbers are verified, it cannot be said that the next number must be like this.

The rigor and precision of mathematics should give scientific proof to any theorem. So Goldbach's conjecture has not become a theorem for hundreds of years, which is why it is famous as a conjecture.

There are several different ways to prove this problem. One of them is to prove that a number is the sum of two numbers, in which the prime factor of the first number does not exceed A and the prime factor of the second number does not exceed B. This proposition is called (a+b).

The ultimate goal is to prove that (a+b) is (1+ 1). 1920, Professor Brown, a Norwegian mathematician, proved by ancient screening method that any even number greater than 2 can be expressed as the sum of the products of nine prime numbers and nine other prime numbers, that is, it proved that (a+b) is (9+9).

1924, German mathematicians proved (7+7); 1932, the British mathematician proved (6+6); 1937, the Soviet mathematician vinogradov proved that an odd number large enough can be expressed as the sum of three odd prime numbers, from which the conclusion of the odd part of Euler's vision was drawn, leaving only the proposition of the even part. 1938, China mathematician Hua proved that almost all even numbers can be expressed as the sum of the powers of a prime number and another prime number.

From 1938 to 1956, Soviet mathematicians successively proved (5+5), (4+4) and (3+3). 1957, China mathematician Wang Yuan proved (2+3); 1962, China mathematician Pan Chengdong and Soviet mathematician Barba independently proved (1+5); 1963, Pan Chengdong, Wang Yuan and Barba proved this point again (1+4).

1965, several mathematicians proved at the same time (1+3). 1966, Chen Jingrun, a young mathematician in China, made an important improvement on the screening method and finally proved it (1+2).

His proof shocked China and foreign countries, and he was praised as "pushing the mountain" and named it "Chen Theorem". He proved the following conclusion: any large enough even number can be expressed as the sum of two numbers, one of which is a prime number, and the other is either a prime number or a product of two prime numbers.

Put it away.

3. Little knowledge of mathematics

1. Percentage of Wang Juzhen

Wang Juzheng, a scientist in China, has a motto about the failure of the experiment, which is called "There is still a 50% hope of success if you continue, and 1000% failure if you don't do it."

2. Tolstoy's music score

Tolstoy, a great Russian writer, compared people to a score when talking about people's evaluation. He said: "A person is like a score, his practical ability is like a numerator, and his evaluation of himself is like a denominator. The larger the denominator, the smaller the value of the score. "

1, the essence of mathematics is its freedom. A poet and lead singer

2. In the field of mathematics, the art of asking questions is more important than the art of answering questions. A poet and lead singer

3. No problem can touch people's emotions as deeply as infinity, and few other concepts can stimulate reason to produce rich thoughts as infinity, but no other concepts need to be clarified as infinity. Hilbert (Hilbert)

Mathematics is an infinite science. Herman Weil

5. Problem is the core of mathematics. Halmos

6. As long as a branch of science can raise a large number of questions, it is full of vitality, and no questions indicate the termination or decline of independent development. Hilbert

7. Some beautiful theorems in mathematics have the following characteristics: they are easy to be summarized from facts, but their proofs are extremely hidden. Gauss

3. Rybakov constant and variables

Russian historian Rybakov said in The Use of Time: "Time is a constant, but for diligent people, it is a' variable'. People who use' minutes' to calculate time spend 59 times more time than people who use' hours'. "

Second, write epigrams with symbols.

4. China's minus sign

When talking about learning and exploration, Hua, a famous mathematician in China, pointed out: "To dare to do subtraction in learning is to subtract what the predecessors have solved and see what problems have not been solved, which requires us to explore and solve."

5. Edison's plus sign

The great inventor Edison used the plus sign to describe genius. He said: "Genius = 1% inspiration +99% sweat."

6. The symbol of dimitrov.

Dimitrov, an internationally renowned worker's movement activist, commented on a day's work: "We should take time to think about what we have done in a day, whether it is' addition' or' subtraction'. If it is' addition', we will make progress; If it is'-',you have to learn from it and take measures. "

Third, aphorisms written in formulas.

7. Einstein formula

Einstein, the greatest scientist in modern times, wrote a formula when talking about the secret of success: a = x+y+z Y+Z. He explained that A stands for success, X stands for hard work, Y stands for the correct method, and Z stands for less empty talk. "

4. A little knowledge about mathematics

Go to Baidu Library to check the complete content > The content comes from users: Wonderful ideas and small knowledge of mathematics * * * 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.

Ninety-nine grids is the multiplication formula we use now. As early as the Spring and Autumn Period and the Warring States Period BC, Jiujiu songs have been widely used by people.

In many works at that time, there were records about Jiujiu songs. The original 99 songs started from "99.8 1" to "22.24", with 36 sentences.

Because it started with "998 1", it was named 99 Song. The expansion of Jiujiu Song to "One for One" was between the 5th century and10th century.

It was in the 13 and 14 centuries that the order of Jiujiu songs became the same as it is now, from "one for one" to "9981". At present, there are two kinds of multiplication formulas used in China. One is a 45-sentence formula, usually called "Xiao Jiujiu"; There is also a sentence 8 1, which is usually called "Big Uncle Nine".

Music and mathematics moving music often give people a wonderful feeling. The ancients said that if the reverberation lingers for three days, it means singing well, and some people sing out of tune because they don't sing well.

Singing the same song, even singing the same song, gives people a very different feeling.

5. Little knowledge of mathematics

Look at Yang Hui Triangle!

Yang Hui Triangle is a triangular numerical table arranged by numbers, and its general form is as follows:

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

1 7 2 1 35 35 2 1 7 1

… … … … …

The most essential feature of Yang Hui Triangle is that its two hypotenuses are all composed of the number 1, and the other numbers are equal to the sum of the two numbers on its shoulders. In fact, ancient mathematicians in China were far ahead in many important mathematical fields. The history of ancient mathematics in China once had its own glorious chapter, and the discovery of Yang Hui's triangle was a wonderful one. Yang Hui was born in Hangzhou in the Northern Song Dynasty. In his book "Detailed Explanation of Algorithms in Nine Chapters" written by 126 1, he compiled a triangle table as shown above, which is called an "open root" diagram. And such triangles are often used in our Olympic Games. The simplest thing is to ask you to find a way. Now we are required to output such a table through programming.