Math knowledge quiz 1. Mathematics interesting knowledge is about 20 to 50 words shorter.

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,

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2. Collection of primary school mathematics knowledge

Summary of knowledge points in primary school mathematics review exam 1. Pupils' knowledge classification of mathematical rules (1) add two digits with a pen, and remember that three 1 are aligned with the same digits; 2. Starting from the unit; 3. When the number of digits reaches 10, enter 1 into ten digits.

(2) Write down the subtraction of two digits and remember the alignment of three digits 1; 2. Reduce from one place; 3. If the number of digits is not enough, subtract 1 from the number of digits, add 10 to the number of digits and then subtract. (3) Mixed operation calculation rule 1. In the formula without brackets, only addition and subtraction or only multiplication and division are done in turn from left to right; 2. In the formula without brackets, if there are multiplication and division and addition and subtraction, the multiplication and division should be calculated first, and then the addition and subtraction should be calculated; 3. If there are brackets in the formula, count the brackets first.

(4) Four-digit reading method 1, starting from the high position, reading thousands, reading hundreds from hundreds, and so on; 2. There is a zero or two zeros in the middle, and only one "zero" is read; No matter how many zeros there are, don't read the last number. (5) The four-digit writing method is 1, which is written in turn from the high position; 2. Write a few words in thousands, a few words in hundreds, and so on. Write "0" in the middle or at the end.

(6) Four-digit subtraction should also pay attention to the alignment of three 1 and the same digit; 2. Reduce from one place; 3. Which figure is not enough to reduce? Retract 1 from the previous position, add 10 to the standard position, and then subtract. (7) Multiplication rule of multiplying one digit by multiple digits 1. Multiplying each of a plurality of numbers by a number in turn starting from a single number; Whoever gets the highest score will be promoted several times.

(8) The divisor rule is single digits 1. Starting from the high division of the dividend, try to divide the first digit of the dividend by the divisor every time. If it is less than the divisor, try to divide the first two digits again. 2. Write the quotient where the divisor is divided; 3. For each quotient, the remainder must be less than the divisor. (9) The multiplication rule with a factor of two digits is 1. First, multiply the number on the two-digit number by another factor so that the last digit of the number is aligned with the two-digit number; 2. Multiply the number on the ten-digit number by another factor to get that the last digit of the number is aligned with the ten-digit number; 3. Then add up the multiplied numbers twice.

(10) The divider is the division rule of two digits 1. Starting from the higher order of the dividend, try to divide the first two digits of the dividend by the divisor. If it is less than the divisor, it is 2. Write the quotient of which number the dividend is divided by; 3. For each quotient, the remainder must be less than the divisor. (1 1) The reading rule of ten thousand volumes series is 1. Read Level 10,000 first, then Level 1; 2, 10,000-level numbers should be read according to the ten-level reading method, and then add a word "10,000" at the back; 3. Don't read the last digit of each level, no matter how many zeros there are. Other numbers have a read-only "zero" with one zero or several consecutive zeros.

(12) Multi-digit reading rule 1, starting from the high position and reading level by level; 2. When reading 100 million or 10,000 levels, read according to a series of reading methods, and then add the words "100 million" or "10,000" at the back; 3. Don't read the zero at the end of each level, other numbers have a zero, or read only one zero for several consecutive zeros. (13) Comparison of decimal sizes To compare the sizes of two decimals, first look at their integer parts, and the number with a large integer part will be large; If the integer parts are the same, the number with large decimal places will be large, so will the number with large decimal places, and so on.

(14) Decimal addition and subtraction calculation method To calculate decimal addition and subtraction, first align the decimal point (that is, align the numbers on the same digit), then calculate by integer addition and subtraction, and finally align the decimal point position on the horizontal line of the obtained number and point the decimal point. (15) Calculation Rule of Decimal Multiplication To calculate decimal multiplication, first calculate the product according to the multiplication law, and then look at the decimal places in the factor. Count from the right side of the product and point to the decimal point.

(16) divisor is the law of integer division. A divider is a fractional division of an integer. Divide according to the law of integer division. The decimal point of quotient should be aligned with the decimal point of dividend. If there is a remainder at the end of the dividend, add 0 to the remainder and continue the division. (17) Division algorithm with divisor as decimal. A divider is a decimal division. First, move the decimal point of the divisor to make it an integer; The decimal point of the divisor is shifted to the right by several digits, and the decimal point of the dividend is also shifted to the right by several digits (the digits are not enough to make up the 0 at the end of the dividend), and then it is calculated by fractional division with the divisor as an integer.

(18) Steps to solve application problems 1: Find out the meaning of the problem, find out the known conditions and problems, analyze the quantitative relationship in the problem, and determine what to calculate first, then what to calculate, and finally what to calculate; 2. Determine how to calculate each step, list formulas and work out numbers; 3. Test and write the answers. (XIX) Enumerate the equation 1 the general steps to solve application problems. Find out the meaning of the problem, find out the unknown, and express it with X; 2. Find out the equal relationship between quantity and quantity in the application problem and make the equation; 3. Solve the equation; 4. Test and write the answers.

(20) The addition and subtraction law of the denominator fraction is the same as that of the denominator fraction, and only the numerator is added and subtracted. (21) Addition and subtraction of fractions with the same denominator Using fractional addition and subtraction, the integer part and the decimal part are added and subtracted respectively, and then the obtained numbers are combined.

(twenty-two) the addition and subtraction of different denominator fractions, the addition and subtraction of different denominator fractions, first calculate the centimeter, and then calculate by the addition and subtraction of the same denominator fraction. (23) Calculation Law of Fraction Multiplying Integer Fraction Multiplies Integer, Molecule is the product of Fraction Molecule Multiplying Integer, and denominator remains unchanged.

(24) Calculation Law of Fractional Multiplication Fractional multiplication, the product of molecular multiplication is the numerator, and the product of denominator multiplication is the denominator. (25) Calculation rule of dividing a number by a fraction A number divided by a fraction is equal to the reciprocal of this number multiplied by the divisor.

(26) Decimals are converted into percentages, and percentages are converted into percentages by moving the decimal point to the right by two places, followed by hundreds of semicolons; Convert percentages to decimals, remove the percent sign, and move the decimal point two places to the left. (27) Fractions are converted into percentages and percentage components. Fractions are usually converted into decimals (except three decimal places) first, and then decimals are converted into percentages; Convert percentages to decimals. First, rewrite the percentage into a fraction with the initials 100, and make a quotation that can be turned into the simplest fraction.

Second, the primary school mathematics mouth determines the meaning classification 1, and what is the circumference of the graph? Surround a graphic office.

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. Various knowledge contests: knowledge contests of Chinese, mathematics, science, history, geography and music.

A, multiple-choice questions (***5 small questions, 6 points for each small question, out of 30 points.

Each of the following questions gives four options codenamed A, B, C and D, of which one and only one option is correct. Please put the code of the correct option in parentheses after the question.

Don't fill it in, fill it in too much or fill it wrong, it's all 0) 1. On the expressway, start from 3 kilometers and pass a speed limit sign every 4 kilometers; And from 10 km, it passes the speed monitoring every 9 km.

Passing through these two facilities at 19 km for the first time, and passing through these two facilities at the same time for the second time is () (A)36 (B)37 (C)55 (D)90 2. Known, and then the value of a is equal to () (A)-5 (B)5 (C)-9 (D)9 3.

The three vertices A, B and C of Rt△A, B and C are all on parabola, and the hypotenuse AB is parallel to the X axis. If the height on the hypotenuse is h, then () (A)h2 4.

A square piece of paper, cut it into two parts along a straight line without any vertices with scissors; Take out a part of it, and then cut it into two parts along a straight line that does not exceed any vertex; Take out one of the three parts, or cut it into two parts along a straight line that doesn't pass through any vertex ... So, 34 62 polygons and some polygons are finally obtained, and then at least the number of knives to be cut is () (A)2004 (B)2005 (C)2006 (D)2007 5. As shown in the figure, the square ABCD is inscribed in ⊙O, the point P is on the bad arc AB, the DP is connected, and the AC is at the point Q. If QP=QO, the value is () (A) (B) (C) (D) 2. Fill in the blanks (***5 small questions, each with 6 points, out of 30 points) 6.

It is known that a, b and c are integers, a+b = 2006 and c-a = 2005. If A0 ............................10 in addition, when a=b, it is given by formula ⑤, that is, the solution is, or. Therefore, the value range of a is, ......................................................................

Proof: Because AC∨PB, so ∠KPE=∠ACE. And PA is the tangent of ⊙O, so ∠KAP=∠ACE. So ∠KPE=∠KAP, so, that is kp2 = ke ka. ............................................................................................

Solution: First, prove the proposition that for any positive integer B 1 19, B2, …, b 1 19, there must be several (at least one or all) sums that are multiples of 1 19. The facts. B 1 b2, …, b 1 b2 … b 1 19, ① If one of ① is a multiple of 1 19, the conclusion holds. If ① is not a multiple of 1 19, then they are. 1 18 is 1 18. Therefore, there must be two identical remainders divided by 1 19. Let's call it b 1 … bi and (1≤i).

5. A little knowledge 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. Especially to understand the basic knowledge and basic learning skills. And review in time to 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 to remember them as much as possible, instead of "reading with uncertain books". 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. Familiar with the thinking of solving various problems. First of all, we practice the basic knowledge repeatedly according to the topic of the textbook, and then find some extracurricular activities to help develop 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 make yourself highly focused and get your brain excited. Quick thinking, entering the best state, and using it freely in the exam. Third, adjust the mentality and treat the exam correctly. First of all, the main focus should be on the basics, basic skills and basic methods, because most exams are based on basic questions, and the more difficult questions also start from the basics. Therefore, only by adjusting your 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 thinking and ensure. We should try our best to get the rare questions right, so that our level can be normal and extraordinary. This shows 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 we can follow these skills to improve our ability and let ourselves enter the ocean of mathematics.

6. 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 =1111/kloc-0. 27 = 333333333 ... 1 2345679 * 81= 999999 These are all 9 times of1multiplied by 9.

And 99, 108, 1 17 to 17 1. The final answer is:12345679 * 99 =1222212345679 *108 =13333333212345677. 444444443 ..... 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 hair themselves 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 a lie.

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.