The complete works of excerpts from fifth grade mathematics manuscripts.

# 5th grade # Introduction In everyday life, people often come into contact with handwritten newspapers. With the help of handwritten newspapers, we can cultivate our innovative consciousness and creativity. The following is carefully arranged for everyone, welcome to read.

1. Excerpted from the fifth-grade Mathematics Manuscript.

Humans gradually have the concept of number, starting with natural numbers. Because people have ten fingers, most ethnic groups have established the decimal representation of natural numbers. Twenty groups are too many and too big, and you have to use your toes at a glance. Five groups are too few and there are too many groups. Ten groups is a more pleasant compromise. There are ancient Babylonian notation, Greek notation, Roman notation and China notation. After 5,000 years of development and progress, Indians invented zero for the first time, and zero plus a natural number was called an integer, which was introduced into the Islamic world and formed the Arabic numerals that are widely used now. It is not until recent decades that computers need binary again. Arithmetic operation only needs the concept of addition. Multiplication is a simplified operation of multiple additions, and subtraction is the inverse operation of addition. Apart from the inverse operation of multiplication, these are the four operations. Division soon leads to the appearance of fractions. Division with decimals such as tens and hundredths is simply expressed as decimals and cyclic decimals. How to express the money owed to others instead of the money owned, resulting in negative numbers? These numbers add up to rational numbers, which can be expressed by the number axis.

For a long time, people thought that the numbers on the number axis were rational numbers. Later, it was found that when the side length of a square was 1, the diagonal length of the square could not be expressed by a rational number. It is the first mathematical crisis to find the corresponding point on the number axis with the compass. 176 1 year, German physicist and mathematician Lambert Lugar strictly proved that π is also an irrational number, so after including irrational numbers, rational numbers and irrational numbers are collectively called real numbers, and the number axis is also called real number axis. Later, it was found that the probability of getting rational numbers was almost zero and the probability of getting irrational numbers was almost 1, and irrational numbers were much more than rational numbers. Why is this happening? Because the objective world we live in is more unreasonable than reasonable. In order to find out what the square root of a negative number is, the imaginary number I was created in the16th century. The imaginary axis and the real axis intersect vertically to form a complex plane, and the number also developed into a complex number consisting of imaginary and real parts. Whether the concept of number will continue to develop remains to be seen.

2. Excerpt from the fifth-grade mathematics handwritten newspaper

Mathematicians Beisecker and Bergman circulated many interesting stories in the same scientific body, which can also be called jokes. Some are true, others are fabricated by disciples and colleagues. These stories are often closely related to the specific majors of scientists. Insiders regard it as some kind of humor, while outsiders find it boring and sometimes even puzzling. Of course, in areas other than science, scientists are completely "dull", giving the world the impression that they have no sense of humor.

Beisecker S. Besicovich (1891-1970) is a geometric analyst with extraordinary creativity. He was born in Russia and studied at Cambridge University in England during World War I. He learned English quickly, but his level was not very good. His pronunciation is not accurate, and according to the habit of learning Russian, there is no article before nouns. One day, he was giving a class to the students, who were whispering and complaining about the teacher's clumsy English. Beisecker looked at the audience and said solemnly, "Gentlemen, there are 50 million people in the world who speak your English, but 200 million Russians speak my English." The classroom suddenly became quiet.

● After leaving Poland, Stefan Bergman (1898- 1977) worked in Brown University, Harvard University and Stanford University successively. He doesn't give many lectures, and his living expenses are mainly maintained by various subject fees. Because he seldom gives lectures, his foreign language can't be exercised, and his spoken and written language is very obscure. But Bergman himself never thought so. He said: "I can speak 12 languages, and English is the best." In fact, he stutters a little, and it is difficult for others to understand what he says. Once he talked with another Polish analyst in his native language, and he was soon reminded: "Let's speak English, maybe it's better."

During the 1950 International Mathematical Congress, an Italian mathematician Cicella accidentally mentioned that a paper by Bergman might add "differentiability hypothesis". Bergman said confidently, "No, it's not necessary. You don't understand my paper." As he spoke, he pulled the other person to make gestures on the blackboard, and his colleagues waited patiently. After a while, Cicero felt that the differentiability hypothesis was still needed. Bergman is more determined, so be sure to explain it carefully. Colleagues echoed: "well, forget it, we are going to have lunch." Bergman shouted, "Don't be stingy-don't eat." (No differentiation, no lunch) Finally Cecella stayed to listen to his argument step by step.

There is evidence that Bergman is always thinking about mathematical problems. At two o'clock in the morning, he called a student's home: "Are you in the library? I want you to check something for me! "

3. Excerpt from the fifth-grade mathematics handwritten newspaper

1, mathematics is science. Gauss 2. Those who aspire to physics do not know that the following points are impossible: first, mathematics, second, mathematics and third. roentgen

3, unlimited! No other problem has touched the human mind so deeply. -D. Hilbert

A mathematician who is not a poet will never be a complete mathematician. -Wilstes

5. Numbers rule the universe. Pythagoras

4. Excerpt from the fifth-grade mathematics handwritten newspaper

Mathematics is a powerful tool for scientific foresight. The solar system has nine tails. Counting from the inside out, the outermost three are Uranus, Neptune and Pluto. Because these three planets are too far away from the earth to be easily seen, they were discovered late.

178 1 year, the British astronomer Herschel discovered Uranus with a telescope. 19th century, when people observed Uranus, they found that its operation was always "unruly" and always deviated from the pre-calculated orbit. To 1845, it has deviated by two points. What is the reason? Mathematician Bessel and some astronomers imagine that there must be a planet outside Uranus, and its gravity interferes with the operation of Uranus. However, the horizon is endless. Where can we find this new planet?

1843, Adams, a 22-year-old student from Cambridge University in England, used calculus and other mathematical tools according to the principle of mechanics. It took 10 months to finally calculate the location of this unknown planet. On June 265438+1October 2 1 day this year, he happily sent the calculation results to Avery, director of Greenwich Observatory in Britain. I didn't expect the director to be a superstitious and authoritative person. He simply looked down on a "nobody" like Adams and took a cold attitude towards him.

A little later than Adams, Levley, a young mathematician at the Paris Observatory in France, solved a system of equations consisting of dozens of equations in 845, and calculated the orbit of this new planet on August 3 1 65438. On September 18 of this year, he wrote to Galle, a staff member of Berlin Observatory who had a detailed star map at that time, and said to him, "Please aim your telescope at Aquarius on the ecliptic, that is, the longitude is 326 degrees, then you will see a ninth-grade star in the area about 1 degree from this point. (The weakest star visible to the naked eye is six stars.) On September 23rd, Galle received a letter from Le Verrier, and that night he observed it according to the position specified by Levi's column. Sure enough, in less than half an hour, he found a star he had never seen before, only 52' away from the position calculated by Li Weilie. After 24 hours of continuous observation, he found that this star is actually a planet, moving among stars. After a period of discussion, all astronomers recognized it as the eighth planet in the solar system and named it Neptune according to the story of Greek mythology. This is the first time that humans have calculated the planet with a pen.

19 15, American astronomer Lowell used the same method to calculate the existence of Pluto, the farthest planet in the solar system. 1930, Thomas of America really discovered this planet.

5. Excerpt from the fifth-grade mathematics handwritten newspaper

First, the smallest number. The ancient and huge family of natural numbers consists of all natural numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. The smallest one is "1", which cannot be found. You can look for it if you are interested.

Second, there are no natural numbers.

Maybe you think you can find a natural number (n), but you will immediately find another natural number (n+ 1), which is greater than n, which means that you will never find a natural number in the family of natural numbers.

Third, "1" is indeed the smallest in the family of natural numbers.

The natural number is infinite, and "1" is the smallest of the natural numbers. Some people disagree that "1" is the smallest natural number, saying that "0" is smaller than "1" and "0" should be the smallest natural number. This is wrong, because natural numbers refer to positive integers, and "0" is a non-positive integer or a non-negative integer, so "0" does not belong to the family of natural numbers. "1" is indeed the smallest in the family of natural numbers.

Don't underestimate the smallest "1", which is the unit of natural numbers and the first generation of natural numbers. Humans first recognized "1", and only by using "1" can we get 1, 2,3,4. ...

I told you the special status of "1", which is the first in a thousand miles. Don't underestimate it.