The Song of Mathematics Knowledge in 1999

1. 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.

2. Nine Jiu Ge 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 gets 4", with 36 sentences.

Because it started with "998 1", it was named 99 Song. The expansion of Jiujiu songs to "11" was between the 5th century and10th century.

It was in the 13 and 14 centuries that the order of Jiujiu songs changed from "one to 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".

3. The circle is a seemingly simple but actually wonderful circle. The ancients first got the concept of circle from the sun and the moon on the fifteenth day of the lunar calendar.

Even now, the sun and the moon are used to describe some round things, such as the Moon Gate, Qin Yue, Moon Shell, Sun Coral and so on. Who drew the first circle? The stone balls made by the ancients more than 100 thousand years ago are quite round.

As mentioned earlier, Neanderthals 18000 years ago used to drill holes in animal teeth, gravel and stone beads, some of which were very round. The caveman used a pointed device to drill a hole, but one side could not get in, and then he drilled from the other side.

The tip of the stone tool is the center of the circle, and half of its width is the radius. Turn around and you can drill a round hole. Later, in the pottery age, many pottery were round.

Round pottery is made by putting clay on a turntable. When people start spinning, they make round stones or ceramic cocoons.

Banpo people (in Xi 'an) built round houses 6000 years ago, with an area exceeding 10 square meter. The ancients also found that rolling logs was more economical.

Later, when they were carrying heavy objects, they put some logs under big trees and stones and rolled them around, which was of course much more labor-saving than carrying them. Of course, because the log is not fixed under the weight, you have to roll the log rolled out from the back to the front and pad it under the front of the weight.

About 6000 years ago, Mesopotamia made the world's first wheel-a round board. About 4000 years ago, people fixed round boards under wooden frames, which was the original car.

Because the center of the wheel is fixed on a shaft, and the center of the wheel is always equal to the circumference, as long as the road surface is flat, the car can move forward in a balanced way. You can make a circle, but you don't necessarily know its nature.

The ancient Egyptians believed that the circle was a sacred figure given by God. It was not until more than 2,000 years ago that China's Mozi (about 468- 376 BC) defined the circle: "One China has the same length".

It means that a circle has a center and the length from the center to the circumference is equal. This definition is 100 years earlier than that of the Greek mathematician Euclid (about 330 BC-275 BC).

Pi, the ratio of circumference to diameter, is a very strange number. The Book of Weekly Calculations says that "the diameter is three times a week", and pi is considered to be 3, which is only an approximate value.

When the Mesopotamians made the first wheel, they only knew that pi was 3. In 263 AD, Liu Hui of Wei and Jin Dynasties annotated Nine Chapters of Arithmetic.

He found that "the diameter is three times that of a week" is just the ratio of the circumference to the diameter of a regular hexagon inscribed in a circle. He founded secant technology, and thought that when the number of inscribed sides of a circle increased infinitely, the circumference was closer to the circumference of a circle.

He calculated the pi = 3927/1250 of the inscribed circle of the regular 3072-sided polygon. Would you please convert it into decimal and see what it is? Liu Hui applied the concept of limit to solving practical mathematical problems, which is also a great achievement in the history of mathematics in the world. Zu Chongzhi (AD 429-500) continued to calculate on the basis of previous calculations, and found that the pi between 3. 14 15926 and 3. 14 15927 was the earliest value in the world accurate to seven decimal places. He also used two fractional values to express pi: 22/7 is called approximate ratio.

Please change these two fractions into decimals and see how many decimals are the same as the known pi today. In Europe, it was not until 1000 years later16th century that the Germans Otto (A.D. 1573) and Antoine Z got this value. Now that there is an electronic computer, pi has been calculated to more than 10 million after the decimal point.

4. Besides counting numbers, mathematics needs a set of mathematical symbols to express the relationship between numbers and shapes. 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 "*", which was first proposed by the British mathematician Authaute at 163 1; One is "",which was first created by British mathematician heriott. German mathematician Leibniz thinks: "*".

2.5 grade mathematics knowledge

A math joke 1. Once, her mother patiently inspired her to do arithmetic: "Ya Ya, have you learned to do subtraction?" Come on, let's see, how much is 4 MINUS 2? ""it's already two o'clock, mom. "

"That's right, good boy. So, what about 5 MINUS 5? " "Five minus five, minus five.

"Ya ya muttered," I won't, mom. "

"Son, you can't! Think about it, for example, you have five coins in your pocket, but suddenly, all five coins fall out. Tell me, what else do you have in your pocket? " Ya Ya blinked her eyes and said, "Did you drop it? Well, there is still a hole in my pocket! " "I always get 100 in arithmetic."

"That's because you learn well." "But I never listen in class."

"That's because you are smart. You will know to study hard when you come home from school." "Smart? A little, but after school, I am a person who deals with football. "

"Then you must have cheated in the exam." "I can't say that. I didn't copy books or peek at others. How can I be derailed? "

"Then what happened to you?" "I kicked Jim, the bookworm in front, in the chair." "If you don't, you won't. How can you be so naughty? "

"I kicked the first foot, and he stretched five fingers back with his hand." "What does this mean?" "The answer to the first question is 2+3."

"Oh ... what if you ask the 5*8 answer to the tenth question?" "It was after I kicked the tenth foot that he stretched out four fingers first and then clenched his fist immediately, so I knew the answer of 40." 3. The teacher announced the results: "Xiaohua scored 30 points, Xiaoming scored 20 points ..." Pig: I got 0 points! Dog: What should I do? Me too ... Pig: We both got the same score in the exam. Will the teacher think we cheated? Legend has it that one day, Zhuge Liang summoned his soldiers and said, "Which one of you chooses an integer from 1 to 1024 and keeps it in mind. I asked ten questions, only one' yes' or' no'.

After answering all ten questions, I will' calculate' the numbers in your mind. "ZhuGeLiangGang say that finish, a counselor stood up and said, he has chosen a good number.

Zhuge Liang asked, "Did you choose more than 5 12?" The counselor replied, "No." Zhuge Liang asked his advisers nine questions in succession, and all the advisers answered them one by one.

Zhuge Liang finally said, "The number you remember is 1." The counselor was surprised because he really chose this number.

Do you know how clever Zhuge Liang is? In fact, the method is very simple, that is, take half of 1024, and the tenth time is "1". According to this truth, you can find the required number by asking ten questions in a row.

3. Mathematical sayings 1. Wang Juzheng's Percentage China scientist Wang Juzheng has a proverb about experimental failure, which says, "There is still a 50% chance of success if you continue, or 100% failure if you don't do it." 2. Tolstoy's score When it comes to people's evaluation, Tolstoy compares people to a score.

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. Cantor) 2. In the field of mathematics, the art of asking questions is more important than the art of answering questions. Cantor) 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. However, no other concept needs clarification like infinity. Hilbert) 4. Mathematics is an infinite science. Hermanville 5. The problem is the core of mathematics. P.R. halmos 6. As long as a branch of science can ask many questions, it is full of vitality. No problem, indicating the termination or decline of independent development. Hilbert 7. Some beautiful theorems in mathematics have such characteristics: they are easy to sum up from facts, but the proofs are extremely profound. Gauss 3. Rybakov's Constants 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'. "

When talking about learning and exploration, Hua, a famous mathematician in China, pointed out: "To dare to do subtraction in learning is to subtract the parts that have been solved by predecessors and see if there are any unsolved problems, which need us to explore and solve." Edison, a great inventor, used a plus sign to describe genius. He said: "Genius = 1% inspiration +99% sweat."

6. dimitrov's symbol dimitrov, an internationally renowned worker movement activist, said in his evaluation of a day's work: "We should spend time thinking 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. " 3. The aphorism written in Formula 7. Einstein Formula When talking about the secret of success, Einstein wrote a formula: A = X+Y+Z Y+Z.

And explained: A stands for success, X stands for hard work, Y stands for correct method, and Z stands for less empty talk. ""If you use a small circle to represent what you have learned and a big circle to represent what I have learned, then the area of the big circle is a little more, but the blank outside the two circles is our ignorance.

The bigger the circle is, the more ignorant faces its circumference contacts. "-Zhi Nuo Cauchy (A.L. Cauchy) People will die, but their deeds will last forever. People will die, but achievements will last forever.

Laplace (1749–1827) is not well known. What we don't know is infinite. C. Hermite1822–1901) Abel left mathematicians enough to keep them busy for 500 years. When commenting on Abel, he once said: "What Abel left behind can keep mathematicians busy for 500 years.

"Poursin (Poisson, Simé on1781-1840)" Life is only good for two things, namely, discovering mathematics and teaching.

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-The symbol "=" was widely used in Leibniz, Germany in the 0/7th century. He also used "∽" to indicate similarity and ""to indicate congruence in geometry.

Greater than sign ">" and less than sign "

4. 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:

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5. 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.

6. Mathematics is fun, little knowledge, 20 to 50 words short.

Interesting knowledge of mathematics

Number theory part:

1, there is no maximum prime number. Euclid gave a beautiful and simple proof.

2. Goldbach conjecture: Any even number can be expressed as the sum of two prime numbers. Chen Jingrun's achievement is that any even number can be expressed as the sum of the products of one prime number and no more than two prime numbers.

3. Fermat's last theorem: n power of x+n power of y = n power of z, and n> has no integer solution at 2 places. Euler proofs 3 and 4, 1995 were proved by British mathematician andrew wiles.

Topology part:

1. The relationship among points, faces and edges of a polyhedron: fixed point+number of faces = number of edges +2, which was proposed by Descartes and proved by Euler, also known as euler theorem.

2. euler theorem's inference: There may be only five regular polyhedrons, namely regular tetrahedron, regular octahedron, regular hexahedron, regular icosahedron and regular dodecahedron.

3. Turn the space upside down, the left-handed object can be changed into the right-handed, and through Klein bottle simulation, a good mental gymnastics,

Excerpted from: /bbs2/ThreadDetailx? id=3 1900

7.20 Mathematical knowledge of words

People call 12345679 a "number missing 8", which has many surprising features, such as multiplying it by a multiple of 9, and the product will be composed of the same number. People call this "uniform". For example:12345679 * 9 =1111165438. 27 = 333333333 ... 1 2345679 * 81= 999999 These are all 9 times of1multiplied by 9. And 99, 108, 1 17 to 650. The answer is:12345679 * 99 =1222212345679 *108 =13333333212345679 *. 444443... 12345679 * 17 1 = 2 1 1 1 165438.