Zu Chongzhi
(429~500 AD)
Zu Chongzhi (429-500) was a mathematician, astronomer, and physicist of the Southern Dynasties during the Northern and Southern Dynasties era in China. Zu Chongzhi's grandfather's name was Zuchang, and he worked as a governor in the Song Dynasty who managed court buildings. Growing up in such a family, Zu Chongzhi read a lot of books when he was young, and people praised him as a knowledgeable young man. He was especially fond of studying mathematics and also astronomical calendars, often observing the sun and the operation of the planets and making detailed records.
Zu Chongzhi studied science tirelessly. His greater achievement was in mathematics. He used to annotate the ancient mathematical work "Nine Chapters of Arithmetic" and write a book "Suffixed Art". His most outstanding contribution was to find out the circumference of the circle with considerable accuracy. After a long period of painstaking research, he calculated pi to be between 3.1415926 and 3.1415927, becoming the first scientist in the world to extrapolate the value of pi to more than seven digits.
Zu Chongzhi is a multi-faceted in scientific invention, he built a guide car, how to turn the car, the car's bronze always pointing to the south; he also built the "thousands of miles of boat", in the new Tingjiang (in the southwest of Nanjing) on the trial voyage, you can sail more than a hundred miles a day. He also used water power to turn the stone mill, pounding rice and grinding grain, called "water pestle and mill".
2. Primary six math knowledge points
Elementary school math is a key stage in the learning career, in order to enable students to make progress in mathematics, I hereby organize the sixth grade math important knowledge points combing for your reference. 一、常用的数量关系式1、每份数*份数=总数 Total ÷ 每份数=份数 Total ÷份数=每份数2、1倍数*倍数=几倍数 Several times ÷ 1 times = multiples Several times ÷ multiples = multiples Several times ÷ multiples = multiples of 1 times 3、速度*时间=路程路程路程 路÷速度=时间 路÷时间=速度4、单价*数量=总价 總价 总价 ÷單价=数量 总价÷数量=单价=数量 总价 ÷数量=单价5、工作效率* Total price ÷ price = quantity Total price ÷ quantity = price 5. Efficiency * working time = total work Total work ÷ efficiency = working time Total work ÷ working time = efficiency 6. Divided number 2, elementary school math graphics formula 1, square (C: perimeter S: area a: side length) perimeter = side length * 4 C = 4a area = side length * side length S = a * a2, square (V: volume a: prism length) surface area = prism length * prism length * 6 S table = a * a * a * 6 volume = prism length * prism length * prism 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, Rectangle (V: Volume s: Area a: Length b: Width h: Height) (1) Surface Area (length*width+length*height+width*height)*2 S=2(ab+ah+bh) (2) Volume=length*width*height V=abh5, Triangle (s: Area a: Bottom h: Height) Area=bottom*height÷2 s= ah÷2 triangle height=area *2÷base triangle base=area *2÷height6, parallelogram (s: area a: base h: height) area=base*height s=ah7, trapezium (s: area a: top base b: bottom base h: height) area=(top+bottom base)*height ÷2 s=(a+b)* h÷28, circle (s: area C: circumference л d=diameter r=radius) (1) circumference= Diameter * л = 2 * л * radius C = лd = 2 лr (2) area = radius * radius * л 9, cylinder (v: volume h: height s: base area r: radius of the base c: perimeter of the base) (1) side area = perimeter of the base * height = ch (2 лr or лd) (2) surface area = side area + base area * 2 (3) volume = base area * high (4) volume = side area ÷ 2 * radius 10 Fractional Decimal * Multiple = Large (or Fractional + Difference = Large) 15, Encounter Problem Encounter distance = Speed and * Encounter Time Encounter Time = Encounter Distance ÷ Speed and Speed and = Encounter Distance ÷ Encounter Time 16, Concentration Problem Weight of Solute + Weight of Solvent = Weight of Solution Weight of Solute ÷ Weight of Solution * 100% = Concentration Weight of Solution * Concentration = Weight of Solution Weight of Solute ÷ Concentration = Weight of Solution 17, Concentration Problems Concentration = weight of solution 17, Profit and Discount Problems Profit = Sold Price - Cost Profit Margin = Profit ÷ Cost * 100% = (Sold Price ÷ Cost - 1) * 100% Up and Down Amount = Principal * Percentage of Increase or Decrease Interest = Principal * Rate of Interest * Time After Tax Interest = Principal * Rate of Interest * Time * (1-20%) III. Common Unit Conversions 1, Unit Conversions for Lengths 1 Kilometer = 1,000 Meters 1 Meter = 10 decimeters 1 decimeter = 10 centimeters 1 meter = 100 centimeters 1 centimeter = 10 millimeters area unit conversion 1 square kilometer = 100 hectares 1 hectare = 10,000 square meters 1 square meter = 100 square decimeters 1 square decimeter = 100 square centimeters 1 square centimeters = 100 square millimeters 2, the body (volume) volume unit conversion 1 cubic meter = 1,000 cubic decimeters 1 cubic decimeters = 1,000 cubic centimeter 1 cubic decimeter = 1 liter 1 cubic centimeter = 1 milliliter 1 cubic meter = 1000 liters Weight unit conversion 1 ton = 1000 kg 1 kg = 1000 grams 1 kg = 1 kilogram RMB unit conversion 1 yuan = 10 cents 1 corner = 10 cents 1 yuan = 100 cents 3. Time unit conversion 1 century = 100 years 1 year = 12 months Big Nation (31 days) There are: 1\ 3\ 5\ 7\ 8\ 10\December Smaller months (30 days) are: 4\6\9\November 28 days in February in a normal year, 29 days in February in a leap year 365 days in a normal year, 366 days in a leap year 1 day = 24 hours 1 hour = 60 minutes 1 minute = 60 seconds 1 hour = 3600 seconds.
3. math trivia less 6th grade book of
1. unit price*quantity=total price 2. unit production*quantity=total production 3. speed*time=distance traveled 4. ergonomics*time=total amount of work Elementary School Math Definition Theorem Formulas (II)
I. Arithmetic
1. Law of Exchange of Addition: two numbers are added and exchanged for the position of the additive, the sum is remains unchanged.
2. The law of combination of addition: three numbers are added together, the first two numbers are added together, or the last two numbers are added together, and then added to the third number, and unchanged.
3. The law of multiplication and exchange: when you multiply two numbers, you exchange the positions of the factors and the product remains the same.
4. Law of Multiplication and Combination: When you multiply three numbers, multiply the first two by each other, or multiply the last two by each other, and then multiply them by the third number, and the product remains the same.
5. The law of multiplication and distribution: two numbers and the same number of multiplication, you can put the two additions with the number of multiplication, and then add the two products, the result is unchanged. For example: (2+4)*5=2*5+4*5.
6. Properties of division: in division, the divisor and the divisor are simultaneously enlarged (or reduced) by the same number of times, the quotient remains unchanged. 0 divides any number that is not 0.
7. Equality: the equation in which the value on the left side of the equal sign is equal to that on the right side of the sign is called the equality formula. The basic property of an equation is that if both sides of the equation are multiplied (or divided) by the same number at the same time, the equation still holds.
8. Equation: An equation containing an unknown number is called an equation.
9. Univariate equation: An equation containing an unknown number, and the number of times the unknown number is once is called a univariate equation.
Learn the example of a one-dimensional equation and calculation. I.e., to exemplify an equation with χ and to calculate it.
10. Fractions: The unit "1" is divided into a number of equal parts, the number of such a part or parts, called a fraction.
11. Addition and subtraction of fractions: fractions with the same denominator, only the numerator is added or subtracted, the denominator remains unchanged. Fractions with different denominators are added and subtracted, and then added and subtracted.
12. Comparison of the size of fractions: fractions with the same denominator, the molecule is large, the molecule is small. Fractions with different denominators are compared, and then compared; if the numerator is the same, the larger denominator is smaller.
13. Multiply a fraction by an integer, using the product of the numerator of the fraction and the integer as the numerator, and the denominator remains unchanged.
14. Multiply a fraction by a fraction, using the product of multiplying the numerators as the numerator and the product of multiplying the denominators as the denominator.
15. Division of a fraction by an integer (other than 0) is equal to multiplying the fraction by the reciprocal of that integer.
16. True fractions: a fraction whose numerator is smaller than its denominator is called a true fraction.
17. False fractions: A fraction whose numerator is larger than the denominator or whose numerator and denominator are equal is called a false fraction. False fraction is greater than or equal to 1.
18. Carried Fractions: False fractions written in the form of integers and true fractions are called carried fractions.
19. Basic Properties of Fractions: When the numerator and denominator of a fraction are multiplied or divided by the same number (except 0), the size of the fraction remains the same.
20. A number divided by a fraction is equal to the number multiplied by the reciprocal of the fraction.
21. A number divided by a number B (except 0) is equal to the reciprocal of the number A multiplied by the number B
4. 6th Grade Math Knowledge Summaries
I. Position In learning about position by using pairs of numbers to determine the location of points, the location of a point was initially determined according to rules and conventions.
Since in a plane rectangular coordinate system, the X-axis is drawn first and the coordinates on the X-axis represent columns. The two numbers are first enclosed in parentheses and then separated by a comma.
The numbers inside the parentheses are, from left to right, the number of columns and the number of rows. The number of columns and rows must be a specific number, not a letter such as (X,5), which represents a horizontal line, and (5,Y) which represents a vertical line, neither of which identifies a point.
This part of the knowledge permeate the mathematical idea of combining numbers and shapes, you can draw a picture on the grid paper. Second, the fraction multiplication Fraction multiplication meaning: 1, the fraction multiplied by an integer is a simple operation to find the sum of several identical additions, with the same meaning as the multiplication of integers.
2, multiplying fractions by fractions is to find a number of how many. Example: How much is 1/4 of a wall brushed at one time, and how much is 1/5 of a wall brushed at one time? Seek 1/5 of 1/4 is how much? Solution 1: use a piece of paper to represent a wall, folded, which is the use of mathematical ideas of combining numbers and shapes.
Solution 2: work efficiency into * work time = total work Algorithm for multiplication of fractions: 1. Fractions multiplied by integers, the product of the numerator multiplied by the integer does the numerator, and the denominator remains unchanged. 2, fractions and fractions multiply, the product of multiplying the numerator with the product of multiplying the numerator, and the product of multiplying the denominator with the product of multiplying the denominator.
Simplification of fractions: the numerator and denominator at the same time divided by their greatest common factor. On the calculation of multiplication of fractions: you can multiply in the process of multiplication, you can also multiply the product of the numerator of the denominator of the product, advocate in the process of calculation, so that simple.
The writing format of the approximate fraction: the two can be divided by first crossing out the number, respectively, in their upper and lower write the number after the approximate fraction. Basic properties of fractions: When the numerator and denominator are multiplied or divided by the same number (except 0), the value of the fraction remains the same.
The significance of the inverse: two numbers whose product is 1 are the reciprocal of each other. Special emphasis: reciprocal, that is, the reciprocal is a relationship between two numbers, they are dependent on each other, the reciprocal can not exist alone.
The method of finding the reciprocal: 1, the reciprocal of the fraction is to exchange the position of the numerator and denominator. 2, the inverse of the integer is to see the integer as a fraction with a denominator of 1, and then exchange the position of the numerator and denominator.
The reciprocal of 1 is itself. Because 1*1=1 0 has no reciprocal.
0 multiplied by any number gives 0=0*1,1/0 (the denominator can not be 0) III. Division of Fractions Division of fractions is the inverse of multiplication of fractions, that is, the product of two numbers is known to be multiplied by one of the factors, and the operation of finding the other factor. Divided by a number is multiplied by the reciprocal of the number, divided by a few is multiplied by a fraction of the number.
Basic properties of division by fractions: emphasize the exception of 0 Ratio: the division of two numbers is also called the ratio of two numbers. Ratio represents the relationship between the two numbers, can be written in the form of a ratio, can also be expressed in fractions, but still read a few than a few.
Note: 10/2 = 5/1, said than read 5 to 1,19:2 = 5, is the ratio, the ratio is a number, can be an integer, a fraction, can also be a decimal. The ratio can represent the relationship between two identical quantities, i.e., a multiplicative relationship.
It can also represent the ratio of two different quantities to get a new quantity. Example: distance/speed = time.
To simplify a ratio: 1. Divide the previous and next terms of the ratio by their greatest common divisor at the same time. 2, For the ratio of two fractions, multiply the antecedent and consequent terms by the lowest common multiple of the denominator at the same time, and then simplify the ratio by simplifying the ratio of integers.
3, the ratio of two decimals, move the decimal point to the right. It is also reduced to an integer ratio first.
In the application section of multiplication of fractions, it is advocated to draw line graphs to analyze quantitative relationships. The known quantities and the problem being asked should be labeled on the graph.
The key is to find the unit "1", drawing line graphs, mainly to find a fraction of a number is how much? Application: find a number more than another number of these questions: first find (or less) a few, and then and the unit "1" (that is, the standard quantity for comparison). (Large - small) / compare the standard (that is, the unit "1") Drawing line graphs: (1) labeled known and unknown.
(2) Analyze quantitative relationships. (3) Find equivalence.
(4) Make equations. Note: Draw two line graphs for the relationship between two quantities and one line graph for the relationship between part and whole.
Even for example: 3:4:5 reads: 3 than 4 than 5 Whether it is an experiment in origami or drawing a line graph, it is actually the language of graphics that reveals the geometric significance of the process of calculating the division of fractions. In learning this knowledge, multiplication and division of fractions, knowledge of ratios, the use of analogical mathematical methods (similarity and variation).
In addition, the data is simple, reducing the difficulty of inquiry, understanding the arithmetic, easy to calculate orally, the whole reasoning process is in the recent development zone of students' thinking ability. Than and division, the difference between fractions: division is an operation, a fraction is a number, than the relationship between two numbers.
The golden mean, the most beautiful point. A C BAC:AB=CB:AC The host is standing on the stage and he works best when he stands at the golden mean point on the stage.
Commonly used to make judgments: a number divided by a number less than 1, the quotient is greater than the number being divided. A number divided by 1 has a quotient equal to the divisor.
When a number is divided by a number greater than 1, the quotient is less than the divisor. IV. Circles Derive the area of a circle, using the transformational idea of gradual approximation.
The more equal (even) parts a circle is divided into, the closer the image is to a rectangle. Embody the idea of turning a circle into a square and a curve into a straight one by applying transformational ideas.
The new for the old, unknown for known, complex for simple, abstract for concrete. When the area is the same, the perimeter of the rectangle is the longest, the square is in the center, and the circumference of the circle is the shortest.
When the perimeter is certain, the circle has the largest area, the square is in the center, and the rectangle has the smallest area.
5. Elementary School Math Grade 6 Lower Level Knowledge Points
Here are my review materials.
1 Number of servings per serving * number of servings = total number of servings Total ÷ number of servings per serving = number of servings Total ÷ number of servings = number of servings per serving 2 Multiple of 1 * number of servings = number of servings Multiples of servings ÷ number of servings = number of servings Multiples of servings ÷ number of servings = number of servings 3 Speed * time = distance traveled Route ÷ speed = time Route ÷ time = speed 4 Price per unit * number of servings = total price Total price ÷ price per unit = number of servings Total ÷ number of servings = number of servings 5 Efficiency of work * working time = work 5 Efficiency * work time = total work Total work ÷ efficiency = work time Total work ÷ work time = efficiency 6 Addition + addition = sum Sum - one addition = another addition 7 Subtracted - subtracted = difference Subtracted - difference = subtraction Difference + subtraction = subtracted 8 Factor * factor = product Product ÷ one factor = another factor 9 Divided ÷ divisor = quotient Divided ÷ quotient = divisor Quotient * divisor = divisor Elementary school graphing formulas 1 Square C Perimeter S Area a Side Length Perimeter = Side Length * 4 C=4a Area = Side Length * Side Length S=a*a 2 Square V: Volume a: Prongs Surface Area = Prong Length * Prong Length * 6 S Surface = a*a*6 Volume = Prong Length * Prong Length * Prong 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 Rectangle V: Volume s: Area a: Length b: Width h: Height (1) Surface area (length*width + length*height + width*height)*2 S=2(ab+ah+bh) (2) Volume=length*width*height V=abh 5 Triangle s Area a Base h Height Area=base*height ÷ 2 s=ah÷2 Triangle Height=area *2 ÷base Triangle base=area *2 ÷height 6 Parallelogram s Area a Base h Height Area = bottom * height s=ah 7 Trapezoid s area a top bottom b bottom h height Area = (top bottom + bottom) * height ÷ 2 s=(a+b) * h ÷ 2 8 Circle S area C perimeter ∏ d=diameter r=radius (1) Perimeter = diameter * pi = 2 * pi * radius C = pi d = 2 pi r (2) Area = radius * radius * pi 9 Cylinders v: Volume h: Height s; Bottom area r: Bottom radius c: Perimeter of base (1) Side area = Perimeter of base * Height (2) Surface area = Side area + Base area * 2 (3) Volume = Base area * Height (4) Volume = Side area ÷ 2 * Radius 10 Cones v: Volume h: Height s; Bottom area r: Bottom radius Volume = Bottom area * Height ÷ 3 Total number ÷ Total number of servings = Mean Equation for Sum and Difference Problems (Sum + Difference)÷2 = Large number (Sum - Difference)÷2=Smaller number Sum Multiples Problem Sum ÷ (multiple-1) = decimal Fractional*multiple = greater (or Sum-decimal = greater) Difference-doubling problem Difference ÷ (multiple-1) = decimal Fractional*multiple = greater (or Fractional+difference = greater) Primary Olympiad formula Formula for sum-difference problem Sum+difference ÷2 = greater (sum-difference) ÷2 = lesser Sum-multiplying problem Sum ÷ (multiple-1) = decimal Fractional*multiplier = greater (or Sum-difference = greater) Difference-multiplying problem Sum ÷ (multiple-1) = decimal Fractional*multiplier = greater (or Sum-difference = greater) (or and - difference = large) Formula for difference-multiplication problems Difference ÷ (multiple-1) = small number Decimal * multiple = large number (or Decimal + difference = large number) Formula for tree-planting problems 1 Tree-planting problems on unenclosed routes can be classified into the following three main scenarios: (1) If trees are to be planted at both ends of an unenclosed route, then (2) If trees are to be planted at one end of a non-closed line and not at the other end, then: Number of plants = Number of segments = Full length ÷ Spacing Full length = Spacing * Number of plants Spacing = Full length ÷ Number of plants (3) If trees are not to be planted at either end of a non-closed line, then: Number of plants = Segments-1 = Full length ÷ Spacing-1 Full length = Spacing * (Number of plants +1) Spacing = Full length ÷ (Number of plants +1) Number of trees to be planted on a closed line The relationship is as follows Number of plants = Number of sections = Total length ÷ Spacing Total length = Spacing * Number of plants Spacing = Total length ÷ Number of plants Equation for the problem of profit and loss (Profit + Loss) ÷ Difference between two allocations = Number of shares participating in the allocation (Profit - loss) ÷ Difference between two allocations = Number of shares participating in the allocation (Loss - loss) ÷ Difference between two allocations = Number of shares participating in the allocation Equation for the problem of meeting Meeting Distance traveled by the meeting = Speed and * Time of the meeting Meeting Meeting Time = Meeting time = Meeting distance ÷ Speed sum Speed sum = Meeting distance ÷ Meeting time Formula for catch-up problem Catch-up distance = Difference in speed * Catch-up time Catch-up time = Catch-up distance ÷ Difference in speed Difference in speed = Catch-up distance ÷ Catch-up time Problem of water flow Velocity = Static water velocity + Currents velocity Counter-current velocity = Static water velocity - Currents velocity Static water velocity = (Currents velocity + Counter-current velocity) ÷ 2 Currents velocity = (Currents velocity - Counter-current velocity) ÷ 2 Concentration problem Formula for concentration problem Weight of solute + weight of solvent = weight of solution Weight of solute ÷ weight of solution * 100% = concentration Weight of solution * concentration = weight of solute Weight of solute ÷ concentration = weight of solution Profit and Discount Formula for profit and discount problem Profit = selling price - cost Profit Margin = Profit ÷ Cost * 100% = (Selling Price ÷ Cost-1) * 100% Amount of increase and decrease = Principal * Percentage of increase/decrease Discount = Actual selling price ÷ Original selling price * 100% (Discount Interest = Principal * Interest rate * Time After tax interest = Principal * Interest rate * Time * (1-20%)
Reference:
The zero at the end of each level is not read out, and the other digits have several consecutive zeros are only read a zero. 2. The way to write integers: from high to low, write one level at a time, and if there is not a unit in any of the digits, write 0 in that digit.
3. The way to read decimals: When reading decimals, read the whole number part in accordance with the reading method of integers, and read the decimal point as a "dot", and read each digit in the decimals part from the left to the right in order. The decimal part reads each digit from left to right. 4. Writing decimals: When writing decimals, the whole number part is written in accordance with the way the whole number is written, the decimal point is written in the lower right corner of the digit, and the decimal part is written out on each digit in turn.
5. reading fractions: when reading fractions, read the denominator first, then read the "fraction" and then read the numerator, the numerator and denominator in accordance with the reading of whole numbers. 6. writing fractions: first read the denominator, then read the "fraction" and then read the numerator. 6. Writing fractions: write the fraction line first, then the denominator, and finally the numerator, according to the way the whole number is written.
7. Percentage reading: when reading a percentage, first read the percent, then read the number in front of the percent sign, read the number according to the whole number. 8. Percentage writing: Percentages are usually not written in the form of fractions, but in the original molecule followed by a percentage sign "%" to indicate.
(B) the rewriting of the number of a larger multi-digit number, in order to read and write conveniently, it is often rewritten as a "million" or "billion" as the unit of the number. Sometimes also according to the need to omit the number after a number, written as an approximation.
1. accurate number: in real life, in order to count the simplicity of a larger number can be rewritten as ten thousand or billion.
6. math and life small paper, the knowledge of the sixth grade book to do a study, content is not limited, if the right
Learning math is to be able to apply in real life, mathematics is used by people to solve practical problems, in fact, mathematical problems arise in life. For example, the natural use of addition and subtraction to buy things on the street, the construction of houses always need to draw drawings. Such problems are countless, this knowledge is generated from life, and finally be summarized into mathematical knowledge, to solve more practical problems. I once read a story about a professor who asked a group of foreign students, "How many times do the minute hand and hour hand coincide between 12:00 and 1:00?" The students took their watches off their wrists and started dialing the hands; when the professor asked the Chinese students the same question, the students applied the math formula. The professor commented, "This shows that the Chinese students' knowledge of mathematics has been transferred from books to their brains, and they are unable to apply it flexibly, and they seldom think of learning and mastering mathematics knowledge in real life. Since then, I have been consciously connecting math with my daily life. One time, my mom made pancakes, and there were two pancakes in the pan. I thought, "Isn't this a math problem? It takes two minutes to cook one pancake, one minute to cook the front and the back, and two pancakes in the pan at the same time, so how many minutes does it take to cook three pancakes at the most? I thought about it, and came to the conclusion that it takes 3 minutes: first put the first and second pancake into the pan at the same time, after 1 minute, take out the second pancake, put in the third pancake, turn the first pancake over; then cook for 1 minute, so that the first pancake is ready, take it out. Then put the opposite side of the second pancake, and at the same time turn the third pancake over, so that it is all done in 3 minutes. I told my mom about this idea, and she said that it's not really that coincidental, there has to be some error, but the algorithm is correct. It seems that we have to apply what we learn in order to make math work in our lives. Math should be learned in life. Some people say that the knowledge in books is not very relevant to the real world. This means that their ability to transfer knowledge has not been fully practiced. It is precisely because they can't understand and apply what they have learned in their daily lives that many people don't pay much attention to math. I hope that students to life to learn mathematics, in life with mathematics, mathematics and life are inseparable, learn deep, learn thoroughly, will naturally find that, in fact, math is very useful.
7. Math trivia, to the sixth grade
1. Yang Hui triangle is a triangular table of numbers arranged in the following general form: 1 1 1 1 1 2 1 1 1 3 3 1 1 1 4 6 4 1 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... The most essential feature of the Yang Hui triangle is that both of its hypotenuse are made up of the number 1, while the rest of the numbers are equal to the sum of the two numbers on its shoulders.
In fact, ancient Chinese mathematicians were way ahead in many important areas of mathematics. The history of ancient Chinese mathematics had its own glorious chapter, and the discovery of Yang Hui's triangle was a very exciting page.
Yang Hui, with the character Qian Guang, was a native of Hangzhou during the Northern Song Dynasty. In his 1261 book "detailed explanation of the algorithm of the nine chapters", recorded the number of triangles as shown above, called "the original source of the method of prescription" map.
And such a triangle is often used in our Olympiads, where the simplest thing to do is to ask you to find patterns. Now we are asked to program the output of such a table of numbers.
2, a story triggered by the mathematician Chen Jingrun a household name in the attack on Goldbach's conjecture made a significant contribution to the creation of the famous "Chen's theorem", so there are many people affectionately referred to as "Prince of Mathematics". Many people affectionately call him the "Prince of Mathematics". But who would have thought that his achievements stemmed from a story.
In 1937, the diligent Chen Jingrun was admitted to Fuzhou Yinghua College, which was during the Anti-Japanese War, the head of the Department of Aeronautical Engineering at Tsinghua University, Dr. Shen Yuan, who stayed in the United Kingdom to go back to Fujian for mourning, did not want to be stranded in his hometown due to the war. Several universities learned of the news, they want to invite Professor Shen forward to lecture, he declined the invitation.
As he was an alumnus of Yinghua, in order to repay his alma mater, he came to this high school to teach math to his students. One day, Mr. Shen Yuan told a story in math class: "200 years ago a Frenchman discovered an interesting phenomenon: 6=3+3,8=5+3,10=5+5,12=5+7,28=5+23,100=11+89.
Every even number greater than 4 can be expressed as the sum of two odd numbers. Since this conclusion is not proven, it is still a conjecture.
The great math Euler said: although I cannot prove it, I am sure that this conclusion is correct. It shines like a beautiful halo of blinding light not far ahead of us.
...... "Chen Jingrun stared, listening to the mesmerized. From then on, Chen Jingrun had a strong interest in this marvelous problem.
After school he loved to go to the library, not only read the middle school tutorials, these university mathematics, science and chemistry course materials he also read hungrily. So he got the nickname "book nerd".
Interest is the first teacher. It is this kind of math story that triggered Chen Jingrun's interest, triggered his diligence, and thus triggered a great mathematician.
3, for science and crazy people As the study of infinity is often introduced to some logical but absurd results (known as "paradox"), many great mathematicians fear to fall into and take the attitude of retreat. In 1874-1876, Cantor, a young German mathematician under 30 years old, declared war on the mysterious infinity.
By the sweat of his brow, he succeeded in proving that a point on a straight line can correspond to a point on a plane as well as to a point in space. In this way, it seems that the points in the 1-centimeter line segment are "as many" as the points on the Pacific Ocean and the points in the entire interior of the Earth. In the following years, Kantor published a series of articles on this kind of "infinite ***" problem, and through rigorous proofs came to many The first is a series of articles on these "infinite ***" problems.
Kantor's creative work and the traditional concept of mathematics has been a sharp conflict, by some people's opposition, attack and even abuse. Some said that Cantor's *** theories were a "disease", that Cantor's concepts were "fog in the mist", and even that Cantor was "crazy".
The enormous mental pressure from the mathematical authorities finally broke Cantor, so that he was mentally exhausted, suffered from schizophrenia, and was admitted to a psychiatric hospital. But the gold was not to be trifled with, and Cantor's ideas finally shone through.
At the first International Conference of Mathematicians, held in 1897, his achievements were recognized, and the great philosopher and mathematician Russell praised Cantor's work as "probably the most gigantic work of which this age can boast." But Cantor was still in a trance, unable to take comfort or joy from the reverence.
On January 6, 1918, Cantor died in a mental hospital. Kantor (1845-1918), born in Petersburg, Russia, a rich merchant family of Danish-Jewish origin, moved to Germany with his family at the age of 10, and had a strong interest in mathematics since childhood.
He received his doctorate at the age of 23 and has been engaged in teaching and researching mathematics ever since. The *** theory he created has been recognized as the foundation of all mathematics.
4. Mathematician's "forgetfulness" On the day of his 60th birthday, Chinese mathematician Prof. Wu Wenjun, as usual, woke up at dawn and spent the whole day immersed in arithmetic and formulas. Someone specially selected the evening of this day to visit the door to pay a visit to the door, after exchanging pleasantries, explain the intention: "Listen to your wife said, today is your 60th birthday, especially to express congratulations."
Wu Wenjun as if listening to a piece of news, suddenly realized that: "Oh, yes? I had forgotten." The visitor was secretly surprised, thinking: the mathematician's brain is filled with numbers, how can he not even remember his own birthday? In fact, Wu Wenjun's memory for dates is very strong.
When he was nearly a year old, he first attacked a difficult problem - "machine proof". This is in order to change the mathematicians "a pen, a piece of paper, a head" way of labor, the use of electronic computers to achieve mathematical proof, so that mathematicians can spare more time to carry out creative work, he was in the process of research on this subject, for the date of installation of electronic computers, computers for the final compilation of more than 300 "instructions". The date of the installation of the electronic computer, the date of the final program for the computer more than three hundred "instructions", are clearly remembered.
Later, when the birthday guest asked him how he couldn't even remember his own birthday, he replied: "I never remember those meaningless numbers. In my opinion, what does it matter if my birthday is one day early or one day late? So, my birthday, my lover's birthday, my child's birthday, I do not remember, he never wanted to celebrate his own birthday or the family's birthday, and even the day of my wedding, I also forgot.
But there are some numbers that have to be remembered, and it's easy to remember them ......" 5, routine steps under the apple tree In the spring of 1884, the young mathematician Adolf Hurwitz came to K?nigsberg from G?ttingen to work as an associate professor at the age of less than 25.