Mathematical knowledge of snowflake 1. Know little about mathematics

A little knowledge of mathematics.

The origin of mathematical symbols

Besides counting, mathematics needs a set of mathematical symbols to express the relationship between number and number, number and shape. The invention and use of mathematical symbols are later than numbers, but they are much more numerous. Now there are more than 200 kinds in common use, and there are more than 20 kinds in junior high school math books. They all had an interesting experience.

For example, there used to be several kinds of plus signs, but now the "+"sign is widely used.

+comes from the Latin "et" (meaning "and"). /kloc-in the 6th century, the Italian scientist Nicolo Tartaglia used the initial letter of "più" (meaning "add") to indicate adding, and the grass was "μ" and finally became "+".

The number "-"evolved from the Latin word "minus" (meaning "minus"), abbreviated as m, and then omitted the letter, it became "-".

/kloc-In the 5th century, German mathematician Wei Demei officially determined that "+"was used as a plus sign and "-"was used as a minus sign.

Multipliers have been used for more than a dozen times, and now they are commonly used in two ways. One is "*", which was first proposed by the British mathematician Authaute at 163 1; One is "",which was first created by British mathematician heriott. Leibniz, a German mathematician, thinks that "*" is very similar to Latin letter "X", so he opposes the use of "*". He himself proposed to use "п" to represent multiplication. But this symbol is now applied to the theory of * * *.

/kloc-In the 8th century, American mathematician Audrey decided to use "*" as the multiplication symbol. He thinks "*" is an oblique "+",which is another symbol of increase.

""was originally used as a minus sign and has been popular in continental Europe for a long time. Until 163 1 year, the British mathematician Orkut used ":"to represent division or ratio, while others used "-"(except lines) to represent division. Later, in his book Algebra, the Swiss mathematician Laha officially used "∫" as a division symbol according to the creation of the masses.

/kloc-in the 6th century, the French mathematician Viette used "=" to indicate the difference between two quantities. However, Calder, a professor of mathematics and rhetoric at Oxford University in the United Kingdom, thinks that it is most appropriate to use two parallel and equal straight lines to indicate that two numbers are equal, so the symbol "=" has been used since 1540.

159 1 year, the French mathematician Veda used this symbol extensively in Spirit, and it was gradually accepted by people. /kloc-In the 7th century, Leibniz in Germany widely used the symbol "=", and he also used "∽" to indicate similarity and ""to indicate congruence in geometry.

Greater than sign ">" and less than sign "

2. 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.

References:

/olpcyanghui

3. Know little about mathematics

It is very difficult for pupils with poor grades to learn primary school mathematics. In fact, primary school mathematics belongs to basic knowledge, and it is relatively easy to master as long as you master certain skills. Primary school is a time to develop good habits, so it is very important to cultivate children's habits and learning ability. What are the skills of primary school mathematics?

First, pay attention to the lecture in class and review it in time after class.

The acceptance of new knowledge and the cultivation of mathematical ability are mainly carried out in the classroom, so we must pay special attention to the efficiency of classroom learning and find the correct learning methods. In the classroom, we must follow the teacher's thinking and actively formulate the following steps to think and predict the difference between the problem-solving thinking and the teacher. In particular, we must understand the basic knowledge and basic learning skills, review them in time, and avoid doubts. First, before all kinds of exercises, we must remember the teacher's knowledge points, correctly understand the reasoning process of various formulas, and try our best to remember instead of using "uncertain books to read". Be diligent in thinking, try to think about some problems with your brain, carefully analyze the problems, and try to solve them by yourself.

Second, do more exercises and form a good habit of solving problems.

If you want to learn math well, you need to ask more questions and be familiar with all kinds of problem-solving ideas. First of all, we practice the basic knowledge repeatedly according to the topic of the textbook, and then find some extracurricular activities to help broaden our thinking practice, improve our analytical ability and master the law of solving problems. For some problems that are easy to find, you can prepare a wrong book for collection, write your own ideas for solving problems, and develop a good habit of solving problems in daily life. Learn to keep yourself highly focused.

Third, adjust the mentality and treat the exam correctly.

First of all, the main focus should be on the foundation, basic skills and basic methods, because most exams are based on basic questions, and the more difficult questions are also based on basic questions. Therefore, only by adjusting the learning mentality and trying to solve problems with clear ideas will there be no too difficult problems. Practice more exercises before the exam, broaden your mind, and improve the speed of doing the questions on the premise of ensuring accuracy. Simple basic questions should be grasped with 20 points. Try to do the right thing on rare topics, so that your level can be normal or extraordinary.

It can be seen that the skill of primary school mathematics is to do more exercises and master basic knowledge. The other is mentality, and it is very important to adjust mentality. So you can follow these skills to improve your ability and enter the ocean of mathematics.

4. 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= 1 1 1 1 1 1 1 1 1

12345679* 18=222222222

12345679*27=333333333

……

12345679*8 1=999999999

These are all 0 times to 9 times of 65438+9.

And 99, 108, 1 17 to 17 1. Finally, the answer is:

12345679*99= 122222222 1

12345679* 108= 1333333332

12345679* 1 17= 1444444443

… …

12345679* 17 1=2 1 1 1 1 1 1 109

It is also a "uniform"

General knowledge of mathematics (reproduced)

[Author: gnwz]

Mathematical common sense

1. 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 own hair 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 deceptive.

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.

5. Little knowledge of mathematics

1, as early as more than 2000 years ago, our ancestors used magnets to make an instrument to indicate the direction. This instrument is Sina.

2. German mathematician kravis was the first to use points as decimal points.

"Tangram" is a jigsaw puzzle in ancient China. It consists of seven thin plates, which can be put together into a big square. The patterns spelled out are varied, and later spread abroad, called Tang Tu.

It is said that as early as 4500 years ago, our ancestors used notch to measure time.

6. China is the first country to use the rounding method.

7. Euclid's most famous work, The Elements of Geometry, is the foundation of European mathematics. It put forward five postulates and developed them into Euclidean geometry, which is widely regarded as the most successful textbook in history.

8. Zu Chongzhi, a mathematician, astronomer and physicist in the Southern Dynasties, ranked the value of pi in the seventh place.

9. Rudolph, a Dutch mathematician, calculated the 35th place of pi.

10 Archimedes, known as the "father of mechanics", has many mathematical works handed down from generation to generation. Archimedes once said: Give me a fulcrum and I can move the earth. This sentence tells us that we should have the courage to find this fulcrum and use it to find the truth.

Extended data

Mathematics (Mathematics or maths, from the Greek word "Má thē ma"; Often abbreviated as "mathematics"), it is a discipline that studies concepts such as quantity, structure, change, space and information, and belongs to a formal science from a certain point of view.

In the development of human history and social life, mathematics also plays an irreplaceable role, and it is also an indispensable basic tool for studying and studying modern science and technology.