The story of the ancestor of mathematicians (AD 429-500), during the Northern and Southern Dynasties, Laiyuan County, Hebei Province. As a child, he read many books on the subject of astronomy, mathematics, worked hard, and practiced hard. Finally, he became an outstanding mathematician and astronomer in ancient China.
Zu Chongzhi’s outstanding achievement in mathematics was the calculation of the ratio of the circumference of a circle to its diameter. During the Qin and Han Dynasties, "a circle with a diameter of 1" was put in front of people. Compared with the circumference of a circle, its diameter was the "ancient rate." Later it was discovered that the ancient error rate was too large. Compared with the circumference of a circle, its diameter should be the diameter of the circle. A Wednesday's Surplus?, but I have a different view. Until the Three Kingdoms period, Liu Hui calculated the circumference of a circle using the scientific method of "circle cutting" to approximate the circumference of a circle inscribed in a regular polygon. After engraving 96 polygons, we obtained π = 3.14, and pointed out that the more the number of sides of a regular polygon, the more accurate the calculation of π value. Based on Zu Chong’s past achievements, he obtained π after hard study and repeated calculations. Between 3.1415926 and 3.1415927
Xu Ruiyun was admitted to the famous Shanghai Girls' High School on June 15, 1915. Xu Ruiyun was born in Shanghai in February 1927. I liked mathematics since I was a child, and graduated from high school in the Department of Applied Mathematics of Zhejiang University in September 1932. In the Department of Mathematics, I was taught by Zhu Shulin, Qian Baocong, Chen Jiangong, and Su Buqing. In addition, there were some lecturers and teaching assistants. . Chen Jiangong and Su Buqing served in mathematics courses. At that time, there were very few students in the mathematics department. There were only five students in her class, but there were also more than a dozen in Thales (ancient Greek mathematician). and astronomer) came to Egypt, and people wanted to test their abilities and asked him if he had the ability to measure the height of the pyramid. Thales said, but there was one condition - the pharaoh must show it. The next day, Pharaoh's pyramid also gathered around it. Many people watched. Qin Lesi came in front of the pyramid and cast his shadow on the ground. Then every now and then he made the length of his shadow measured, and when the measurement matched his height, he immediately made a mark on it. The projection of the Great Pyramid on the ground and then measuring the distance from the projection of the spire to the base of the pyramid, he quoted the exact height of the pyramid. The Pharaoh asked him to explain how from "the length of the shadow is equal to the length of the tower shadow is equal to the height of the tower." "Principle, what is known today as the similar triangle theorem.
Archimedes
, the goldsmith made a pure gold crown in Syracuse, Elotiniwang, The inner suspicion was mixed with silver, and then asked Archimedes to identify it. When he entered the bathtub, the water from the outer basin overflowed, and then realized that the objects of different materials, although the weight was the same, but the amount of water would not drain equally. Based on this principle, we can judge whether the official is adulterated.
Gallois was born in a small town far away from Paris. His father was the principal of a school and the mayor of the family for many years. Galois was always courageous and fearless. In 1823, the 12-year-old Galois left his parents to study in Paris. He was not satisfied with the strict classroom indoctrination and found his own original research in the most difficult mathematics. They are all of great help to him. The teacher's evaluation should only be in the forefront of mathematics.
The most outstanding mathematician of the 20th century, von Neumann, invented the electronic computer in 1946. , which has greatly promoted the progress of science and technology, and greatly promoted the progress of social life. In 1911, von Neumann played a key role in inventing the computer, which his westerner father called "the computer" in 1921. von Neumann was highly regarded by the teacher who appeared during his reading at the Luse Len High School in Budapest. Feicht was tutored by individual teachers and collaborated on published mathematical papers with von Neumann when he was younger than 18 years old.
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About the discovery of irrational numbers
The Pythagoreans of ancient Greece believed that any number in the world is an integer or a fraction, which is what they One of the creeds, one day, a member of the school Hippasus suddenly discovered that the length of the diagonal side of the square was an unfamiliar number, so he studied hard and finally proved that it cannot be an integer or a fraction. , but this broke the creed of the Pythagoreans, so to complete the order of Grasius, he allowed the rumor, but when Hibbs revealed the secret, Pythagoras was furious and wanted him dead. Hibbers accelerated its flight, but was caught and thrown into the sea, sacrificing its precious life for scientific development. Hibbers discovered that such numbers are called irrational numbers. The discovery of irrational numbers was the first mathematical crisis and made a significant contribution to the development of mathematics.
Chinese history, mathematics
/gt; Mathematics is an important subject in ancient Chinese science. According to the characteristics of the development of ancient Chinese mathematics, it can be divided into five stages: embryonic state; system The formation, development, prosperity and the integration of Chinese and Western mathematics
The buds of ancient Chinese mathematics
The primitive commune and finally private ownership and production of commodity exchange, the concepts of number and shape have further In the later period of the original commune in 1234, the pottery unearthed during the Yangshao Culture period has been engraved with symbols, and written symbols have begun to replace knotted ropes to record events.
The pottery unearthed in Xi'an Banpo has a pattern of 1.8-point equilateral triangles, covering an area of ??100 small squares. The foundations of the houses at the Banpo site are all round and square. In order to draw a circle, Naoto also created prescribed moments for parties to determine, a guide, a rope and other mapping and measuring tools. The "Records of the Summer Century" records that Xia Yu had to use these tools for flood control.
In the middle of the Shang Dynasty, the decimal number in the oracle bones was expressed, and the largest number was 30,000; at the same time, people composed of Yin Tong's 10 heavenly stems and 12 earthly branches remembered 60 days from the day of rebirth; In the Zhou Dynasty, there were 60 names of Jiazi, Yichou, Bingyin and Dingmao. Eight kinds of development hexagrams represented 64 things, including the yin and yang symbols and the eight trigrams.
In the first century BC, the "Zhou Bi Suan Jing" refers to the time measured in the early Western Zhou Dynasty. The depth, width and distance of the three strands, four strings and five circles of the wolfberry hook can be said to be Examples of circles. The "Book of Rites" article mentions that the children of the Western Zhou aristocrats from the age of 9 will have to learn numbers and counting methods from the book, and they will have to receive rituals, music, archery, jade, books, and number "six arts" have become specialized courses.
In the Spring and Autumn Period, the Lawyer's widespread use of the Lawyer's decimal notation system was of epoch-making significance in the development of world mathematics. During this period, the production of measurement mathematics was widely used and increased accordingly. Mathematics.
The contention of a hundred schools of thought during the Warring States period also promoted the development of mathematics, especially the disputes over the rectification of names and some propositions directly related to abstract concepts other than the original entity master nouns. "If the critical moment is not square, it may not be a circle." Big one (infinity) is defined as "no outside", and "small" (infinitely small) is defined as "within a small range." The proposition that "a whip full of whips, if you take half of it every day, will always be inexhaustible."
The Mohist name is derived from the material, and the name can reflect the Mohist mathematical definition of the object from different angles and different depths, such as round, square, flat, straight, time (tangent), end ( point) etc.
The Mohists disagreed and put forward a "half" proposition to refute the proposition: if the line segment is divided into half, the other half will be infinite, and it is inevitable that there will be a "half country" where people can no longer be divided. Not half a point.
's famous proposition discusses the changes in Mohist's proposition that finite length can be divided into infinite sequences. The result of this infinite division is Mohist's mathematical definition and discussion of mathematical propositions, which are ancient Chinese mathematics. The development of theory is of great significance. The formation of ancient Chinese mathematical system
The rising feudal society, economy, and culture developed rapidly during the Qin and Han Dynasties.
The ancient Chinese mathematical system, which was formed during this period, is characterized by the fact that arithmetic has become a specialized subject, and the emergence of the mathematical work "Liu Hui."
"Nine Chapters of Arithmetic" was created and Consolidating the development process of mathematics and summarizing the achievements of mathematics in the feudal society of the Warring States, Qin and Han Dynasties, it is known as the masterpiece of world mathematics. The four arithmetic operations of fractions, this technology (3) Western rules, square root and cube root (including numerical solutions). Quadratic equations) income less than surgery (Xishuang method), various area and volume formulas, solutions to systems of linear equations, rules of operation for positive and negative numbers in addition and subtraction, solutions of Gou Guxing (especially Pythagorean Theorem looking for the Pythagorean number), and the level is very high. The barrister-centered, independent system formed by the rules of subtraction of positive and negative numbers is a characteristic of the world's leading mathematical development. Completely different from the mathematics of ancient Greece.
"Nine Chapters on Arithmetic" has several notable features: sub-chapters of mathematical problem sets; expressing arithmetic and algebraic formulas from lawyers; rarely involving the properties of graphics. , emphasis on application and lack of theoretical explanation.
These characteristics are closely related to the social conditions and academic thoughts of the time. During the Qin and Han Dynasties, all science and technology should be to establish and consolidate the feudal system, and to develop social production services. , emphasizing the application of mathematics. ?Finally, a book in the Eastern Han Dynasty, "Nine Chapters on Arithmetic", excluded the great importance of Mohist discussions in the Warring States Period and emphasized the importance of logic in the current production and close integration of mathematical problems with life. The solution is completely in line with the development of society
Mathematics is everywhere in life
The wonders of the world, there are many interesting things in our country of mathematics, for example, in the ninth. Quantity workbook, I have a question, the question goes like this: "A bus drives from east to west 45 kilometers per hour line and stop line 2.5 hours, then only 18 kilometers; the midpoint of the two things City, distance from city, kilometers on both sides? Wang Xing smiled and said that in solving this problem, the calculation methods and results are different. Wang Xing’s calculation of kilometers was less kilometers and Xiaoying’s calculation, but Teacher Xu said there were two results. Why? Are you coming? Also list the counting results of both of them. "Actually, one way we can solve this problem very quickly is: 45×2.5 = 112.5 (km), 112.5 18 = 130.5 (km) and 130.5×2 = 261 (km), but a closer look looks The feeling is incorrect. In fact, in this case, we have ignored a very important condition, which is "just 18 kilometers from the city at the midpoint of time". There is no such thing as the word "from". Say the midpoint, or the midpoint above. If the column is not the midpoint of the midpoint of 18 kilometers, the column is 45 -18 = 94.5 (km), 94.5×2 = 189 (km). Therefore, the correct answer should be: 45×2.5 = 112.5 (km), 112.5 18 = 130.5 (km), 130.5×2 = 261 (thousands) meters) and 45×2.5 = 112.5 (kilometers), 112.5-18 = 94.5 (kilometers), 94.5×2 = 189 (kilometers). The two answers are arbitrary, plus Xiaoying’s answer is comprehensive. .
In daily study, the answers to many math questions are often easily ignored in exercises or exams, which requires us to study the questions carefully, awaken life experience, carefully consider them, and fully understand them. question correctly, otherwise it is easy to ignore other answers and make an incomplete mistake. In
Interesting Math Questions
1. 1, 2 and 11. 12, 22, 21 4 Two-digit total emissions.
2. Three digits 1, 2, 3. Total emissions __ 27___ A three-digit number.
3. . Discharge ___ ^ 4_____ four numbers 1, 2, 3, 4 in total.
BR/gt;The heart of the home tumbler lock is made of 5 metal cylindrical rods of different lengths. I asked: Is the key of this metal cylinder a rod different from the door lock? The total number of door locks is __5^5__. ___ ^ 10___
5. , and then what is different is the key lock core composed of 10 metal cylinder locks of different lengths.
Observe the following sets of calculations and study the law. You have discovered that this formula contains the natural number n.
(1) 2×2 = 4
1×3 = 3
(2) 5×5 = 25
4 ×6 = 24...
(3)(-2)(-2)= 4
(-1)(-3)= 3
......
____ N * N = (N-1) * (N 1) 1 ____
____ (-N) * (N) = (2 -N)*(1-N) 1 ____________
BR /gt; Figure, in the quadrilateral ABCD, ∠BAD = 60°, ∠B =∠D = 90°, BC = 11, CD = 2. The long-sought diagonal AC.
/gt; ∠CAD = β, ∠CAB = 60°-β
DC / AC = sinβ, BC / AC = SIN ∠CAB = SIN (60°-β)
AC = DC /sinβ= BC /sin (60°-β) Substituting BC = 11 CD = 2
Common denominator (cent) 22/2sin22/11sinβ= (60° gt of -β); 11sinβ=2sin(60°-β)=√3cosβ-sinβ
The beginning is tanβ=√3/12, another CD=2, also AD=8√3
According to the Pythagorean Theorem AC = 14