Everyone looks down on me and thinks that I am dispensable. Sometimes I don't study, and sometimes I am 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?
Since human hands have ten fingers, human beings have 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. ...
Mathematically, it is customary to call this unit of 1/60 "minute", which is represented by the symbol "'"; 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.
Self-report of length unit
One day, the brothers of the length unit got together for a meeting. Big brother "Kilometer" presided over the meeting. First of all, he made a speech: "Our unit of length is the international family. Today, our ethnic minorities are strangers to us. So, let's introduce ourselves first. " First, a man stood up from the center of the meeting and said, "My name is Yin, which is the unit length of China nationality. The ancient book Hanshu: China Faji Lizhi has my name, so I am very old! It is the abbreviation of China's ancient Chinese nation's' city citation', which is 1 km (km) = 30 (city citation). " Then I sat down. Then a "unit" stood up from a corner of the conference room and shouted, "My name is code, which is a British unit of length. The English translation of "code" is 1 code = 3 feet, 1 mile = 1760 code. The relationship with the metric system and the municipal system is: 1 code = 0.9144m = 2.743 city feet. " After the speech of "Code", it was said one after another. "My name is jie, a stateless person. In other words, every country is my nationality, because I am an international nautical speed unit, which can also be used to measure the speed of water and underwater weapons (such as torpedoes). I can't live without length. The sea is my father and time is my mother. 1 section = 1 section. For example, the speed of a ship relative to still water is 15 knots, then its speed is 15 knots. " "My name is Chain, and I am a special soldier who measures short distances at sea. I am one tenth of a nautical mile. " "My name about who also have never heard of! My name is Xun; The special unit for measuring water depth in marine survey can also be said to be stateless, 1 Xun =1100 chain =11000 nautical miles = 1.852 meters. " "My name is Maji, I am Japanese, and I am also a unit of length. I am a member of the family of international units of length, but my face is very strange. So we don't see much (town = 1/36 days, 1 km = 9. 167 town = 0.2546 days). " After everyone finished speaking, "Kilometers" said, "Very good! We knew each other the first time we met. Let's go back to our posts! Continue to play our respective great roles. "
The "ruler" of the human body
Do you know that?/You know what? Do you know that?/You know what? Each of us carries several rulers. If the length of your "one foot" is 8 cm and the length of your desk is 7 feet, you know that the desk is 56 cm. If you take a step of 65 cm, when you go to school, count how many steps you take, and you can figure out how far it is from your home to school. Height is also a ruler. If your height is 150 cm, then you are holding a big tree and your hands are just closed. The length of this tree is about 150 cm. Because everyone's arms are flat, the length and height between the fingertips of both hands are similar. If you want to measure the height of a tree, shadows can also help you. You only need to measure the length of the shadow of the tree and your own shadow. Because the height of the tree = shadow length × height ÷ graph length. Why is this? Learn the proportion and you will understand. If you go to play, if you want to know how far the mountain ahead is from you, you can ask the sound to help you measure it. Sound can travel 33 1 meter per second, so you can hear the echo by shouting at the mountain for a few seconds. Multiply the time to hear the echo by 33 1 and divide by 2. Learning to use these rulers on you is very beneficial for you to calculate some problems. It will also provide convenience for your daily life. You should think about it!
Arabic numerals
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 later spread to Arabia and Europe. Europeans mistakenly think that it was invented by Arabs, so it is called "Arabic numerals". Because they have been circulating for many years, people still call them Arabic numerals.
Now, Arabic numerals have become the universal digital symbols all over the world.
multiplication table
Jiujiuge 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".
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 "-".
It is also said that wine merchants use "-"to indicate how much a barrel of wine costs. After the new wine is poured into the vat, a vertical line is added to the "-",which means that the original line is erased, thus becoming a "+"sign.
/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 "x", which was first proposed by British mathematician orcutt on 163 1; One is "",which was first created by British mathematician heriott. Leibniz, a German mathematician, thinks that "×" is like the Latin letter "X", so he opposes it and agrees to use "×". He himself proposed to use "п" to represent multiplication. But this symbol is now applied to set theory.
/kloc-In the 8th century, American mathematician Audley decided to use "×" as the multiplication symbol. He thinks "×" is "+"written obliquely, 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.
The square root number was once represented by the combination of the first and last letters of the Latin "root". /kloc-At the beginning of the 0/7th century, the French mathematician Descartes used "√" for the first time in his Geometry. "R" is a variant of the Latin word line "R", and "-"is a closed line.
/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 "
Mathematical problems in the world cup
When the World Cup in Korea and Japan was in full swing, did you find many math problems in the World Cup? Do not believe, you look down.
In the World Cup group match, every four teams play a single round robin match. In each game, the winning team scored 3 points, the losing team scored 0 points, and each team scored 1 point. After the group stage, the two teams with high total points qualify and enter the next round. If the total scores are the same, they should be sorted according to further rules.
Question 1:
How many points must a team accumulate to qualify for the next round?
Four teams have to play six games in a single round robin, each game will generate at most 3 points, and six games will generate at most 18 points.
If one team scores 6 points, there are still 12 points left, and there may be two other teams with 6 points each, so they will be sorted according to further rules, so this team may not qualify.
I've figured it out: if one team scores 7 points, it leaves 1 1 points, so it's impossible for two of the other three teams to score more than 7 points, so this team will definitely qualify. Therefore, if a team wants to advance to the next round, it must get at least 7 points to ensure the inevitable qualifying.
Question 2:
One team only scored 3 points. Is it possible for this team to qualify?
It's possible. All six games were draws, and all four teams only scored 3 points. According to the further rules, if the team is in the top two, it is possible to qualify.
There is another situation, can you think of it?
Think about it: (1) If a team scores 5 points, can it qualify? Why?
(2) Can a team qualify with 2 points? Why?
Son, have you ever thought about these questions when watching the World Cup? In fact, mathematics is everywhere in life. As long as you pay attention to it, you will gain a lot.
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