Weight is a measure of the size of an object subjected to gravity. Weight and mass are different, and the unit is Newton. This is the basic property of an object. Under the gravity of the earth, the weight of a substance with a mass of 1 kg is 9.8 Newton.

Because of gravity, an object has a downward force, which is called gravity, also called weight. Due to the gravity of the earth, the latitude and height on the earth are different, and the weight of objects is slightly different. The poles are larger than the equator, and the heights are smaller than the lows. In the same area, the attraction is the same and the weight of the object is the same.

Weight is a measure of the force of an object under the action of gravity. Weight and quality are different. The unit is kilogram weight. Under the gravity of the earth, weight and mass are equivalent, but the units of measurement are different. A substance with a mass of 1 kg is called 1 kg when it is subjected to an external force of1Newton. As a physical concept, what is the exact meaning of weight? Different opinions exist in teaching materials, which leads to confusion in the usage of "polysemy". Under the gravity of the earth, a substance with a mass of 1 kg produces a weight of 9.8 Newton.

Note: Weight only indicates the magnitude of gravity, not the direction of gravity.

2. A little knowledge about mathematics

Discovery of negative numbers

People often encounter various quantities with opposite meanings in their lives. For example, there are surpluses and deficits in accounting; When calculating the rice stored in the granary, sometimes you should remember the grain and sometimes you should remember the valley. For convenience, people think that numbers have opposite meanings. So people introduced the concepts of positive number and negative number, and recorded the excess money as positive number of grain and the loss of money and grain as negative number. It can be seen that both positive and negative numbers are produced in production practice.

According to historical records, as early as 2000 years ago, China had the concept of positive and negative numbers and mastered the arithmetic of positive and negative numbers. When people calculate, they use some small bamboo sticks to put out various figures to calculate. These small bamboo sticks are called "computing chips" and can also be made of bones and ivory.

Liu Hui, a scholar in China during the Three Kingdoms period, made great contributions to the establishment of the concept of negative numbers. Liu Hui first gave the definitions of positive numbers and negative numbers. He said: "Today's gains and losses are the opposite, and positive and negative numbers should be named." This means that when you encounter quantities with opposite meanings in the calculation process, you should distinguish between positive numbers and negative numbers.

Liu Hui gave the method of distinguishing positive and negative numbers for the first time. He said: "The front is red and the negative is black; Otherwise, "evil difference" means that the number of red stick pendulum represents positive number, and the number of black stick pendulum represents negative number; You can also use a stick with an oblique pendulum to represent negative numbers, and a stick with a positive pendulum to represent positive numbers.

In China's famous ancient mathematical monograph "Nine Chapters of Arithmetic" (written in the first century AD), the law of addition and subtraction of positive and negative numbers was put forward for the first time: "Positive and negative numbers say: the same name is divided, different names are beneficial, positive and negative; Its synonyms are divided, the same name is beneficial, nothing is positive, nothing is negative. " Name here is a number, division is subtraction, mutual benefit and division are the addition and subtraction of the absolute values of two numbers, and nothing is zero.

In the present words: "the addition and subtraction of positive and negative numbers is: the subtraction of two numbers with the same sign equals the subtraction of their absolute values, and the subtraction of two numbers with different signs equals the addition of their absolute values." Zero minus a positive number is a negative number, and zero minus a positive number. The addition of two numbers with different signs equals the subtraction of their absolute values, and the addition of two numbers with the same sign equals the addition of their absolute values. Zero plus positive equals positive, zero plus negative equals negative. "

This statement about the arithmetic of positive and negative numbers is completely correct and completely in line with the current law! The introduction of negative numbers is one of the outstanding contributions of mathematicians in China.

The habit of using numbers of different colors to represent positive and negative numbers has been preserved until now. At present, red is generally used to represent negative numbers. The newspaper reports that a country's economy is in deficit, which shows that its expenditure is greater than its income and it has incurred financial losses.

Negative numbers are antonyms of positive numbers. In real life, we often use positive numbers and negative numbers to represent two quantities with opposite meanings. In summer, the temperature in Wuhan is as high as 42℃, and you will feel that Wuhan is really like a stove. The minus sign of the temperature in Harbin in winter is -32℃, which makes you feel the cold in winter in the north.

In the current textbooks for primary and secondary schools, the introduction of negative numbers is through arithmetic operation: a negative number can be obtained by subtracting a larger number from a smaller number. This introduction method can have an intuitive understanding of negative numbers in special problem scenarios. In ancient mathematics, in the process of solving algebraic equations, negative numbers are often produced. The algebraic study of ancient Babylon found that the Babylonians did not put forward the concept of negative root when solving equations, that is, they did not use or find the concept of negative root. In the works of Diophantine, a Greek scholar in the 3rd century, only the positive root of the equation was given. However, in China's traditional mathematics, negative numbers and related arithmetic were formed earlier.

In addition to the positive and negative operation methods defined in Nine Chapters Arithmetic, Liu Hong (AD 206) at the end of the Eastern Han Dynasty and Yang Hui (126 1) in the Song Dynasty also discussed the addition and subtraction principles of positive and negative numbers, all of which were completely consistent with those mentioned in Nine Chapters Arithmetic. It is particularly worth mentioning that in Yuan Dynasty, Zhu Shijie not only explicitly gave the rules of addition and subtraction of positive and negative numbers with the same sign but different signs, but also gave the rules of multiplication and division of positive and negative numbers.

Negative numbers are recognized and recognized abroad, much later than at home. In India, it was not until AD 628 that the mathematician Yarlung Zangbo realized that negative numbers can be the root of quadratic equations. In Europe, Qiu Kai, the most successful French mathematician in the14th century, described negative numbers as absurd numbers. It was not until the17th century that the Dutchman Jirar (1629) first realized and used negative numbers to solve geometric problems.

Unlike China's ancient mathematicians, western mathematicians are more concerned about the rationality of the existence of negative numbers. In the 16 and 17 centuries, most mathematicians in Europe did not admit that negative numbers were numbers. Pascal thinks that subtracting 4 from 0 is sheer nonsense. Pascal's friend Ahrend put forward an interesting argument against negative numbers. He said (-1):1=1:(-1), then how can the ratio of smaller numbers to larger numbers be equal to the ratio of larger numbers to smaller numbers? Until 17 12, even Leibniz admitted that this statement was reasonable. Wally, a British mathematician, acknowledged negative numbers and thought that negative numbers were less than zero and greater than infinity (1655). He explained it this way: Because of a>0, Augustus de Morgan, a famous British mathematician, still thinks that negative numbers are fictitious in 183 1. He used the following example to illustrate this point: "My father is 56 years old and my son is 29 years old. When will the father be twice as old as his son? " Simultaneous equation 56+x=2(29+x), x=-2 is solved. He called the solution absurd. Of course, in Europe in the18th century, not many people refused negative numbers. With the establishment of integer theory in19th century, the logical rationality of negative numbers was really established.

3. A little knowledge 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 "

4. Provide some math knowledge (area, volume, weight, etc. ), such as a male 5. Little knowledge of 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.

6. A little knowledge about mathematics

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.

At the same time, this is also the law of quadratic coefficient of each term after polynomial (A+B) n is opened, that is

0(a+b)^0 0 NCR 0)

1(a+b)^ 1 1 NCR 0)( 1 NCR 1)

2(a+b)^2(2 NCR 0)(2 NCR 1)(2 NCR 2)

3 votes (A+B) 3 (3 abstentions) (3 abstentions 1) (3 abstentions and 2 abstentions) (3 abstentions and 3 abstentions)

. . . . . .

Therefore, the Y term of X layer of Yang Hui triangle is directly (y nCr x).

It is not difficult for us to get that the sum of all terms in layer X is 2 x (that is, when both A and B in (A+B) x are 1).

[the above y x refers to the x power of y; (a nCr b) refers to the number of combinations]

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. Specific usage will be taught in the teaching content.

In foreign countries, this is also called Pascal Triangle.

7. All the knowledge about mathematics

The self-report of "O" is looked down upon by everyone, who thinks that I am dispensable. Sometimes what I should read is not read, and sometimes it is crossed out in the calculation.

But you know what? I also have a lot of real meaning. 1. I said "No".

When counting objects, if there is no object to count, it must be represented by me. 2. I have a digital role.

When counting, if there is no unit in a certain place of the number, I will take it. For example, in 1080, if there is no unit of hundreds or digits, use: 0 to occupy a position.

I mean the starting point. The starting point of ruler and scale is what I express.

4. I mean the boundaries. On the thermometer, my top is called "above zero" and my bottom is called "below zero".

5. I can express different accuracy. In the approximate calculation, I can't just cross out the end of the decimal part.

For example, the accuracy of 7.00, 7.0 and 7 is different. 6. I can't tell.

It's troublesome for me to go to the branch, because it's meaningless for me to go to the branch. Later, you will learn a lot about my special nature and children. Please don't look down on me.

Why do electronic computers use binary? Because there are ten fingers in human hands, human beings invented decimal notation. However, there is no natural connection between decimal system and electronic computer, so it is difficult to be unimpeded in the theory and application of computer.

Why on earth is there no natural connection between decimal and computer? What's the most natural way to count your computer? This should start with the working principle of computers. The operation of the computer depends on the current. For circuit nodes, only two states of current flow: power-on and power-off.

Computer information storage commonly used hard disk and floppy disk. For each recording point on the disk, there are only two states: magnetized and unmagnetized. In recent years, the practice of recording information with optical discs has become more and more common. An information point on an optical disc has two physical states: concave and convex, which play the roles of focusing and astigmatism respectively.

It can be seen that all kinds of media used by computers can show two states. If you want to record a decimal number, there must be at least four recording points (there can be sixteen information states), but at this time, six information states are idle, which will inevitably lead to a great waste of resources and funds. Therefore, decimal system is not suitable as a digital carry system for computers.

So what kind of carry system should we use? People get inspiration from the invention of decimal system: since every medium has two states, the most natural decimal system is of course binary. Binary counting has only two basic symbols, namely 0 and 1.

You can use 1 for startup and 0 for shutdown; Or 1 means magnetized, and 0 means unmagnetized; Or 1 stands for pits, and 0 stands for bumps. In a word, a binary number just corresponds to an information recording point of a computer medium.

In the language of computer science, one bit of a binary system is called a bit and eight bits are called a byte. It is natural to use binary inside the computer.

But in human-computer communication, binary has a fatal weakness-the writing of numbers is particularly lengthy. For example, decimal number 100000 is written as binary number11010100000.

In order to solve this problem, two auxiliary carry systems-octal and hexadecimal are also used in the theory and application of computers. Three digits in binary are recorded as one digit in octal, so that the length of the number is only one third of that in binary, which is similar to that in decimal.

For example, 100000 in decimal is 303240 in octal. A number in hexadecimal can represent four numbers in binary, so a byte is exactly two numbers in hexadecimal.

Hexadecimal system needs to use sixteen different symbols. In addition to the ten symbols of 0 to 9, six symbols of A, B, C, D, E and F are commonly used to represent (decimal) 10,1,12, 13 and 6553 respectively. In this way, the decimal of 100000 is written in hexadecimal, which is 186A0.

The conversion between binary and hexadecimal is very simple, and the use of octal and hexadecimal avoids the inconvenience caused by lengthy numbers, so octal and hexadecimal have become common notation in human-computer communication. Why are the units of time and angle in hexadecimal? The unit of time is hours, and the unit of angle is degrees. On the surface, they are completely irrelevant.

However, why are they all divided into small units with the same names as parts and seconds? Why do they all use hexadecimal? When we study it carefully, we will know that these two quantities are closely related. It turns out that ancient people had to study astronomy and calendars because of the needs of productive labor, which involved time and angle.

For example, to study the change of day and night, it is necessary to observe the rotation of the earth, where the angle of rotation is closely related to time. Because the calendar needs high precision, the unit of time "hour" and the unit of angle "degree" are too large, so we must further study their decimals.

Both time and angle require its decimal units to have the properties of 1/2, 1/3, 1/4, 1/5, 1/6, etc. Can be an integer multiple of it. The unit of 1/60 has exactly this property.

For example: 1/2 equals 30 1/60, 1/3 equals 20 1/60, 1/4 equals 15 1/60 ... Mathematics. The unit of 1/60 of1is called "second", which is represented by the symbol "1229 1". Time and angle are expressed in decimal units of minutes and seconds.

This decimal system is very convenient in representing some numbers. For example, 1/3, which is often encountered, will become an infinite decimal in decimal system, but it is an integer in this carry system.

This hexadecimal decimal notation (strictly speaking, the sixty abdication system) has been used by scientists all over the world for a long time in the astronomical calendar, so it has been used until today. One day, the brothers of the length unit got together for a meeting, and the big brother "Kilometer" presided over the meeting. It spoke first: "Our unit of length is the international family. Today is a minority in our big family, and people are very strange to us. So, let's introduce ourselves first. "

First, someone stood up from the center of the meeting and said, "My name is Yin, right.