Chungchi Tsu

(429 ~500 AD)

Zu Chongzhi (429-500) was a mathematician, astronomer and physicist in the Southern Dynasties of China. Zu Chongzhi's grandfather, Zuchang, was an official in charge of royal architecture in the Song Dynasty. Zu Chongzhi grew up in such a family and learned a lot from childhood. People all praise him as a knowledgeable young man. He especially likes studying mathematics, and he also likes studying astronomical calendars. He often observes the movements of the sun and planets and makes detailed records.

Zu Chongzhi studied science tirelessly. His greater achievement is in mathematics. He once annotated the ancient mathematics book Nine Chapters Arithmetic and wrote a book Composition. His most outstanding contribution is to get quite accurate pi. After a long and arduous study, he calculated pi between 3. 14 15926 and 3. 14 15927, becoming the first scientist in the world to calculate pi to more than seven digits.

Zu Chongzhi is a generalist in scientific inventions. He built a kind of compass, and the copper man in the car always pointed south. He also built a "Thousand-Li Ship" and tried it in Xinting River (now southwest of Nanjing). It can sail 100 Li a day. He also used hydraulic power to rotate the stone mill, pounding rice and grinding millet, which was called "water hammer mill".

2. Main points of mathematics knowledge in the sixth grade of primary school

Primary school mathematics is the key stage of learning career. In order to make students make achievements in mathematics, I am here to sort out the important knowledge points of mathematics in the sixth grade of primary school for your reference. First, the commonly used quantitative relationship 1, each copy * number of copies = total number of copies ÷ each copy = total number of copies ÷ number of copies = 2 per copy, 1 multiple * multiple = multiple ÷ 1 multiple = multiple. Time = distance distance ÷ speed = time distance ÷ time = speed 4, unit price * quantity = total price ÷ unit price = total quantity ÷ quantity = unit price 5, work efficiency * working hours = total workload ÷ work efficiency = working hours ÷ total workload ÷ working hours = work efficiency 6. Factor * factor = product ÷ one factor = another factor 9, dividend ÷ divisor = quotient dividend ÷ quotient = divisor * divisor = dividend II. Calculation formula of primary school mathematical figures 1, square (c: perimeter s: area a: side length) perimeter = side length. A*6 volume = side length * side length * side length V=a*a*a3, rectangle (c: perimeter s: area a: side length) perimeter = (length+width) *2 C=2(a+b) area = length * width S=ab4, cuboid (v: volume s: area a:) 2÷ triangle bottom = area height =ch(2лr or лd) (2) surface area = lateral area+bottom area *2(3) volume = bottom area * height (4) volume = lateral area÷2 * radius 10, cone (v: The formula of sum-difference problem (sum+difference) ÷2= large number (sum-difference) ÷2= decimal 13, sum-times problem and ÷ (multiple-1)= decimal * multiple = large number (or sum-decimal = large number) 60. Encounter problem Encounter distance = speed and * encounter time = encounter distance ÷ sum of speed and speed = encounter distance ÷ encounter time 16, concentration problem Solute weight+solvent weight = solution weight ÷ solution weight * 100%= concentration solution weight * concentration = solute weight. Profit and discount problem Profit = selling price-cost profit rate = profit/cost * 100%= (selling price/cost-1)* 100% fluctuation amount = principal * fluctuation percentage interest = principal * interest rate * interest after tax = principal * interest rate *. Length unit conversion 1 km =1000m1m =1decimeter1decimeter =10cm1cm5438+. 00sqm65438kg 1 kg = 1000g 1 kg RMB unit conversion 1 yuan = 10 angle/kloc-0 angle =10 minute/kloc-0. The time unit is converted into 1 century = 100 1 year =1February (3 1 day):1\ 3 \ 5 \ 7 \ 8 \/kloc-0.

3. Sixth-grade students with little knowledge of mathematics.

1. unit price * quantity = total price 2. Single output * quantity = total output 3. Speed * time = distance 4. Working Efficiency * Time = Total Workload Mathematical Definition Theorem Formula (2)

First of all, arithmetic.

1. additive commutative law: Two numbers are added to exchange the position of addend, and the sum is unchanged.

2. The law of addition and association: When three numbers are added, the first two numbers are added first, or the last two numbers are added first, and then the third number is added, and the sum remains unchanged.

3. Multiplication and exchange law: when two numbers are multiplied, the position of the exchange factor remains unchanged.

4. Multiplication and association law: When three numbers are multiplied, the first two numbers are multiplied, or the second two numbers are multiplied first, and then the third number is multiplied, and the product remains unchanged.

5. Multiplication and distribution law: When two numbers are multiplied by the same number, you can multiply the two addends by this number respectively, and then add the two products, and the result remains unchanged. Such as: (2+4)*5=2*5+4*5.

6. Nature of division: In division, the dividend and divisor are expanded (or reduced) by the same multiple at the same time, and the quotient remains unchanged. Divide 0 by any number other than 0 to get 0.

7. Equation: An equation in which the value on the left of the equal sign equals the value on the right of the equal sign is called an equation. Basic properties of the equation: When both sides of the equation are multiplied (or divided) by the same number at the same time, the equation is still valid.

8. Equations: Equations with unknowns are called equations.

9. One-dimensional linear equation: An equation with an unknown number of 1 is called a one-dimensional linear equation.

Example method and calculation of learning linear equation of one variable. That is, an example is given to illustrate that the formula is replaced by χ and calculated.

10. Score: divide the unit "1" into several parts on average, and the number representing such a part or points is called a score.

1 1. Addition and subtraction of fractions: add and subtract fractions with denominator, only add and subtract numerators, and the denominator remains unchanged. Fractions of different denominators are added and subtracted, first divided, then added and subtracted.

12. Comparison of fraction size: Compared with the fraction of denominator, the numerator is large and the numerator is small. Compare the scores of different denominators, divide them first and then compare them; If the numerator is the same, the denominator is big and small.

13. Fractions are multiplied by integers, and the product of the multiplication of fractions and integers is a numerator, and the denominator remains unchanged.

14. Fractions are multiplied by fractions, the product of numerator multiplication is numerator, and the product of denominator multiplication is denominator.

15. Fraction divided by integer (except 0) equals fraction multiplied by the reciprocal of the integer.

16. True fraction: The fraction with numerator less than denominator is called true fraction.

17. False fraction: the fraction with numerator greater than denominator or numerator equal to denominator is called false fraction. False score is greater than or equal to 1.

18. With score: write the false score as an integer, and the true score is called with score.

19. The basic nature of the fraction: the numerator and denominator of the fraction are multiplied or divided by the same number at the same time (except 0), and the size of the fraction remains unchanged.

20. A number divided by a fraction is equal to the number multiplied by the reciprocal of the fraction.

2 1.A divided by b (except 0) equals the reciprocal of a multiplied by b.

4. The sixth grade mathematics knowledge induction

First of all, the position is determined by several pairs when learning the position. First, determine the location according to regulations and practices.

Because in the plane rectangular coordinate system, the x axis is drawn first, and the coordinates on the x axis represent columns. First enclose two numbers in brackets, and then separate them with commas.

The numbers in brackets are the number of columns and rows from left to right. The number of columns and rows must be specific numbers, and cannot be represented by letters such as (x, 5) representing horizontal lines and (5, y) representing vertical lines, neither of which can determine a point.

This part of knowledge permeates the mathematical thought of combining numbers and shapes, and a picture can be drawn on square paper. Second, fractional multiplication Fractional multiplication means: 1, and fractional multiplication by integer is a simple operation to find the sum of several identical addends, which has the same meaning as integer multiplication.

2. the score multiplied by the score is to find the score of a number. Example: How many times do you brush a wall with 1/4 and 1/5? What is the 1/4 of 1/5? Scheme 1: Use a piece of paper to represent a wall, and fold it up, that is, use the mathematical idea of combining numbers and shapes.

Scheme 2: Work efficiency becomes * working hours = total workload. Fractional multiplication algorithm: 1. Fractions are multiplied by integers. The product of multiplication of a numerator and an integer is a numerator, and the denominator remains the same. 2. Fractions are multiplied by fractions, the product of numerator multiplication is numerator, and the product of denominator multiplication is denominator.

Simplification of fractions: numerator and denominator are divided by their greatest common factor at the same time. About the calculation of fractional multiplication: We can divide the points in the process of multiplication, and we can also divide the numerator and denominator of the product. Division is advocated in the calculation process, which is simple and convenient.

Writing format of reduction: first, cross out two numbers that can be reduced, and write the reduced numbers above and below respectively. The basic property of a fraction: when the numerator and denominator are multiplied or divided by the same number (except 0), the value of the fraction remains unchanged.

Meaning of reciprocal: Two numbers whose product is 1 are reciprocal. Special emphasis: reciprocal, that is, reciprocal is the relationship between two numbers. They are interdependent and reciprocity cannot exist alone.

Method of finding the reciprocal: 1. Finding the reciprocal of a fraction is the position of the denominator of the exchange numerator. 2. To find the reciprocal of an integer is to regard the integer as a fraction with a denominator of 1, and then exchange the positions of the denominator of the molecule.

The reciprocal of 1 is itself. Because 1* 1= 1 0 has no reciprocal.

Multiply 0 by any number to get 0=0* 1, 1/0 (denominator cannot be 0). 3. Fractional division Fractional division is the inverse operation of fractional multiplication, that is, the operation of finding another factor by knowing the product of two numbers and one of them. Dividing by a number is the reciprocal of this number, and dividing by a few is the fraction of this number.

The basic nature of fractional division: emphasizing zero exclusion ratio: the division of two numbers is also called the ratio of two numbers. The ratio represents the relationship between two numbers, which can be written in the form of ratio or expressed in fraction, but still read several ratios.

Note: 10/2=5/ 1, which means that the ratio is 5 1 and 19: 2 = 5, which is a ratio, and the ratio is a number, which can be an integer, a fraction or a decimal. The ratio can represent the relationship between two identical quantities, that is, the multiple relationship.

You can also use the ratio of two different quantities to represent a new quantity. For example: distance/speed = time.

Simplified ratio: 1, and the first and second terms of the ratio are divided by their greatest common divisor at the same time. 2. The ratio of two fractions is simplified as the last term in the previous paragraph multiplied by the least common multiple of the denominator at the same time, and then the integer ratio is simplified.

3, the ratio of two decimal places, move the decimal point position to the right. It is also converted into an integer ratio first.

The application part of fractional multiplication advocates drawing line segments to analyze quantitative relations. Known quantities and problems to be solved should be marked on the diagram.

The key is to find the unit "1" and draw a line graph, mainly to find out what is the score of a number? Application: Find how much one number is more than another: Find (or less) how much first, and then compare it with the unit "1" (that is, the standard quantity). (Large number-decimal number)/comparison standard (i.e. unit "1") Line drawing: (1) Mark the known and unknown.

(2) Analyze the quantitative relationship. (3) Find the equivalence relation.

(4) Column equation. Note: Draw two line graphs for the relationship between two quantities, and draw one line graph for the relationship between part and whole.

For example, 3: 4: 5 is pronounced as 3:4:5. Both origami experiment and line drawing are actually a graphic language, which reveals the geometric significance of fractional division calculation process. In learning these knowledge, the knowledge of fractional multiplication and division and ratio, and the mathematical methods of analogy (similarity and variation) should be used.

In addition, the data is simple, which reduces the difficulty of exploring and understanding arithmetic and is convenient for oral calculation. The whole reasoning process is in the recent development zone of students' thinking ability. The difference between ratio, division and fraction: division is an operation, fraction is a number, and ratio represents the relationship between two numbers.

Golden section, the most beautiful point. A C BAC:AB=CB:AC host stands on the stage, and he stands in the golden section of the stage, with the best effect.

Often used as a judgment: when a number is divided by a number less than 1, the quotient is greater than the dividend. When a number is divided by 1, the quotient equals the dividend.

When a number is divided by a number greater than 1, the quotient is less than the dividend. Fourthly, the area of the circle is deduced by using the transformation idea of gradual approximation.

The more shares a circle is divided into, the closer it is to a rectangle. Reflect the idea of turning a circle into a square and a curve into a straight line, and apply the idea of transformation.

Turn the new into the old, the unknown into the known, the complex into the simple, and the abstract into the concrete. When the area is the same, the perimeter of a rectangle is the longest and the center of a square is the shortest.

When the perimeter is fixed, the circular area is the largest, the square is in the middle and the rectangular area is the smallest.

5. Knowledge points of mathematics in the sixth grade of primary school.

The following is my review materials.

1 * copies per share = total copies/total copies/copies = 2 1 multiple * multiple = multiple1multiple = multiple/multiple = 1 multiple 3 speed * time = distance \ Quantity = total price ÷ total price ÷ unit price = total price ÷ quantity = unit price 5 Work efficiency * Working time = total work amount ÷ work factor = product ÷ one factor = another factor 9 Divider ÷ Divider = quotient dividend ÷ quotient = divisor quotient * Divider = dividend elementary school mathematics. 6 volume = side length * side length * side length V=a*a*a 3 rectangle c perimeter s area a side length perimeter = (length+width) *2 C=2(a+b) area = length * width S=ab 4 cuboid v: volume s: area a: length b: width h: height (1). Volume = length * width * height V=abh 5 triangle s area a bottom h high area = bottom * height ÷2 s=ah÷2 triangle height = area * 2 bottom triangle bottom = area * 2 height 6 parallelogram s area a bottom h high area = bottom * height s=ah 7 trapezoid s area a top bottom b bottom. H ∏ 2 8 circular S area c perimeter ∏ d= diameter r= radius (1) perimeter = diameter *∏=2*∏* radius C=∏d=2∏r (2) area = radius * radius * \ Bottom area r: bottom radius c: bottom perimeter (1) lateral area = bottom perimeter * height (2) surface area = lateral area+bottom area *2 (3) volume = bottom area * height (4) volume = lateral area ÷2* radius 10 cone v: volume h: height. Base area r: base radius volume = base area * height ÷3 total number ÷ total number = formula (sum+difference) ÷2= large number (sum-difference) ÷2= sum of decimal and multiple problems ÷ (multiple-1)= decimal * multiple. Multiplication = large number (or decimal+difference = large number) Elementary school mathematical formula and difference problem formula (sum+difference) ÷2= decimal and multiple problem formula and ÷ (multiple-1)= decimal * multiple = large number (or sum-decimal) multiple = large number formula (or decimal+difference = large number). If trees are planted at both ends of the non-closed line, then: number of plants = number of segments+1= total length ÷ plant spacing-1 total length = plant spacing * (number of plants-1) plant spacing = total length ÷ (number of plants-1) 𖲕 Then: number of plants = number of segments-1= total length ÷ plant spacing-1 total length = plant spacing * (number of plants+1) plant spacing = total length ÷ (number of plants+1) 2 The quantitative relationship of tree planting problem on the closed line is as follows. Number of plants and plant spacing = total length ÷ number of plants profit and loss problem's formula (surplus+deficit) ÷ difference between two distributions = number of shares participating in distribution (large surplus-small surplus) ÷ difference between two distributions = number of shares participating in distribution (large deficit-small deficit) ÷ difference between two distributions = formula of meeting problem of shares participating in distribution = meeting distance. Meeting time Meeting time = Meeting distance ÷ Sum of speed and speed = Meeting distance ÷ Meeting time The formula of tracing problem is: tracing distance = speed difference * catching time = catching distance ÷ speed difference = catching distance ÷ catching time Water problem downstream speed = still water speed+water flow speed = still water speed = (downstream speed+countercurrent speed) \ 100%= concentration solution weight * concentration = solute weight ÷ concentration = solution weight profit and discount problem formula profit = selling price-cost profit rate = profit ÷ cost * 100%= (selling price-cost-1) * 65438.

Baidu knows how to read and write the number 1. Integer reading method: from high to low, read step by step. When reading the 110 million level, first read according to the reading method of the 100 million level, and then add a word "100 million" or "10 thousand" at the end.

The zeros at the end of each stage are not read, and only a few zeros of other digits are read. 2. Writing of integers: from high to low, writing step by step. If there is no unit on any number, write 0 on that number.

3. Decimal reading method: When reading decimals, the integer part is read by integer reading method, the decimal point is read as "dot", and the decimal part reads the numbers on each digit from left to right in sequence. 4. Decimal writing: When writing decimals, the integer part is written as an integer, the decimal point is written in the lower right corner of each digit, and the decimal part is written on each digit in turn.

5. How to read fractions: When reading fractions, read the denominator first, then the "fraction", and then the numerator. Both numerator and denominator read integers. 6. How to write the fraction: write the fraction first, then the denominator, and finally the numerator and the integer.

7. Reading method of percentage: When reading percentage, read the percentage first, and then read the number before the percentage symbol. When reading, read it as an integer. 8. Writing of percentage: percentage is usually expressed by adding a percent sign "%"after the original molecule instead of a fraction.

(2) rewrite a large multi-digit, which is often rewritten as a number in units of "10,000" or "100 million" for convenience of reading and writing. Sometimes, if necessary, you can omit the number after a certain number and write it as an approximation.

1. exact number: in real life, for the convenience of counting, a larger number can be rewritten into tens of thousands or hundreds of millions.

6. Essays on mathematics and life, the knowledge of the first volume of the sixth grade, do a research, the content is not limited, if it is right,

Learning mathematics should be used in real life. Mathematics is used by people to solve practical problems. In fact, there will be math problems in life. For example, when you go shopping, you will naturally use addition and subtraction, and you always have to draw drawings to build a house. There are countless such problems, and all this knowledge comes from life. Finally, it is summed up into mathematical knowledge to solve more practical problems. I once saw a report that a professor asked a group of international students, "6544. Those students all took off their watches from their wrists and began to set hands; When the professor tells the same question to the students in China, the students will use mathematical formulas to calculate. The commentary said that it can be seen that China students' mathematical knowledge is transferred from books to their brains, so they can't use it flexibly. They seldom think of learning and mastering mathematics knowledge in real life. Since then, I have consciously linked mathematics with my daily life. Once, my mother baked a cake and could put two cakes in the pot. I think it takes two minutes to bake a cake, one minute in front and one minute in the back. At most, two cakes are put in the pot at the same time. How many minutes does it take to bake three cakes at most? I thought about it and came to the conclusion that it takes 3 minutes: first, put the first cake and the second cake into the pot at the same time, 1 minute later, take out the second cake, put the third cake and turn the first cake over; Bake 1 min, and the first cake will be ready. Take it out. Then put the reverse side of the second cake, turn the third cake upside down, and it will be all done in 3 minutes. I told my mother this idea, and she said it wouldn't be so clever. There must be some errors, but the algorithm is correct. It seems that we must apply what we have learned to make mathematics better serve our lives. At present, the knowledge in books has little connection with reality. This shows that their knowledge transfer ability has not been fully exercised. It is precisely because they can't understand it well and apply it in daily life that many people don't attach importance to mathematics. I hope that students can learn mathematics in their lives and use mathematics in their lives. Mathematics is inseparable from life. If they study thoroughly, they will naturally find that mathematics is actually very useful.

7. Little knowledge of mathematics, for the sixth grade.

1, Yang Hui triangle is a triangle table arranged by numbers. The general form is as follows:11113314641151. 1 561721353521kloc-0/........................................................................... Yanghui triangle's most essential feature is that its two hypotenuses are all composed of the number1,and the rest are equal to the sum of its upper two numbers.

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.

2. Mathematicians triggered by a story Chen Jingrun, a famous mathematician, made great contributions to overcoming Goldbach's conjecture and founded the famous "Chen Theorem", so many people affectionately called him "the prince of mathematics". But who would have thought that his achievement originated from a story?

1937, diligent Chen Jingrun was admitted to Huaying College in Fuzhou. At this time, during the period of War of Resistance against Japanese Aggression, Professor Shen Yuan, director of the Department of Aeronautical Engineering in Tsinghua University, returned to Fujian to attend the funeral, unwilling to stay in his hometown because of the war. Several universities got the news and wanted to invite Professor Shen to give lectures. He declined the invitation.

As he is an alumnus of Huaying, he came to this middle school to teach mathematics to his classmates in order to report to his alma mater. One day, Teacher Shen Yuan told us a story in math class: "A Frenchman discovered an interesting phenomenon 200 years ago: 6 = 3+3, 8 = 5+3, 10 = 5+5, 12 = 5+7, 28 = 5+23.

Every even number greater than 4 can be expressed as the sum of two odd numbers. Because this conclusion has not been proved, it is still a guess.

Euler said: Although I can't prove it, I am sure this conclusion is correct. It is like a beautiful light ring, shining with dazzling brilliance in front of us not far away.

..... "Chen Jingrun stare eyes, absorbed. From then on, Chen Jingrun became interested in this wonderful question.

In his spare time, he likes going to the library. He not only read the counseling books in middle schools, but also eagerly read the textbooks of mathematics and physics courses in these universities. Therefore, he got the nickname "bookworm".

Interest is the first teacher. It is such a mathematical story that aroused Chen Jingrun's interest and his diligence and made him a great mathematician.

3. People who are crazy about science, because of endless research, often get some logical but absurd results (called "paradoxes"), and many great mathematicians take an evasive attitude because they are afraid of falling into it. During the period of 1874- 1876, Cantor, a young German mathematician less than 30 years old, declared war on the mysterious infinity.

With hard sweat, he successfully proved that points on a straight line can correspond to points on a plane one by one, and can also correspond to points in space one by one. In this way, it seems that there are "as many" points on the 1 cm long line segment as there are points in the Pacific Ocean and the whole earth. In the following years, Cantor published a series of articles about this kind of "infinite * * *" problem, and drew many amazing conclusions through strict proof.

Cantor's creative work has formed a sharp conflict with the traditional mathematical concept, which has been opposed, attacked and even abused by some people. Some people say that Cantor's theory of * * * is a kind of "disease", Cantor's concept is "fog in fog", and even Cantor is a "madman".

Great mental pressure from the authority of mathematics finally destroyed Cantor, making him exhausted, suffering from schizophrenia and being sent to a mental hospital. True gold is not afraid of fire, and Cantor's thought finally shines.

At the first international congress of mathematicians held in 1897, his achievements were recognized, and Russell, a great philosopher and mathematician, praised Cantor's work as "probably the greatest work that can be boasted in this era." But at this time, Cantor was still in a trance, unable to get comfort and joy from people's reverence.

1918 65438+1October 6th, Cantor died in a mental hospital. Cantor (1845- 19 18) was born in a wealthy family of Danish Jewish descent in Petersburg, Russia. /kloc-moved to Germany with his family at the age of 0/0, and was interested in mathematics since childhood.

He received his doctorate at the age of 23 and has been engaged in mathematics teaching and research ever since. His theory of * * * is considered as the basis of all mathematics.

4. Mathematicians' "forgetfulness" On the 60th birthday of Professor Wu Wenjun, a mathematician in China, as usual, he got up at dawn and buried himself in calculations and formulas all day. Someone specially chose to visit at home this evening. After greeting, he explained his purpose: "I heard from your wife that today is your sixtieth birthday, and I came to congratulate you."

Wu Wenjun seemed to hear a message and suddenly said, "Oh, really? I forgot. " The bearer was secretly surprised and thought, how can a mathematician not even remember his birthday because his mind is full of numbers? In fact, Wu Wenjun has a good memory for dates.

Nearly sixty years old, he conquered a difficult problem for the first time-"machine certificate". This is to change the working mode of "a pen, a piece of paper, a head" for mathematicians, and realize mathematical proof with electronic computers, so that mathematicians have more time to do creative work. In the course of his research on this subject, he clearly remembers the date of installing the electronic computer and compiling more than 300 "instruction" programs for the computer.

Later, when a birthday visitor asked him in a chat why he couldn't even remember his birthday, he replied knowingly, "I never remember those meaningless numbers." In my opinion, what does it matter if the birthday is one day earlier and one day later? So, I don't remember my birthday, my wife's birthday, my child's birthday. He never wants to celebrate his or his family's birthday, even my wedding day.

However, some figures must be remembered, and it is easy to remember ... "5. Routine steps under the apple tree 1884 1984 In the spring of 1984, Adolf leonid hurwicz, a young mathematician, came to Koenigsberg from Gö ttingen as an associate professor, when he was less than 25 years old.