Urgently ask for the preface of the mathematical tabloid.

Questioner: Fu Xin-the story of a mathematician recommended by first-class netizens; Zu Chongzhi (AD 429-500) was born in Laiyuan County, Hebei Province during the Northern and Southern Dynasties. He read many books on astronomy and mathematics since childhood, studied hard and practiced hard, and finally made him an outstanding mathematician and astronomer in ancient China.

Zu Chongzhi's outstanding achievement in mathematics is about the calculation of pi. Before the Qin and Han Dynasties, people used "the diameter of three weeks a week" as pi, which was called "Gubi". Later, it was found that the error of Gubi was too large, and the pi should be "the diameter of a circle is greater than the diameter of three weeks". However, there are different opinions on how much is left. Until the Three Kingdoms period, Liu Hui put forward a scientific method to calculate pi-"secant" which approximated the circumference of a circle with the circumference inscribed by a regular polygon. Liu Hui calculated that the circle inscribed by a 96-sided polygon is π=3. 14, and pointed out that the more sides inscribed by a regular polygon, the more accurate the π value is. On the basis of predecessors' achievements, Zu Chongzhi worked hard and repeatedly calculated that π was between 3. 14 15926 and.

Xu Ruiyun, 19 15 was born in Shanghai, and 1927 was admitted to Shanghai famous public girls' middle school in February. Xu Ruiyun liked mathematics since he was a child, but he was more interested in mathematics when he was in middle school. So, 1932 entered the mathematics department of Zhejiang University after graduating from high school in September. At that time, the professors in the Department of Mathematics of Zhejiang University were Zhu, Qian Baoyu, Chen and Su. Besides, there are several lecturers and teaching assistants. The courses in the Department of Mathematics are mainly taught by Chen and Su. There were few students in the department of mathematics at that time. There were five students in two classes in the last session, and this time she was only a dozen.

Thales (an ancient Greek mathematician and astronomer) came to Egypt. People wanted to test his ability, so they asked him if he could measure the height of the pyramids. Thales agreed, but on one condition-Pharaoh must be present. The next day, Pharaoh arrived as scheduled and many onlookers gathered around the pyramid. Before Cyrus came to the pyramids, the sun cast his shadow on the ground. Every once in a while, he asked someone to measure the length of his shadow. When the measured value is completely consistent with his height, he immediately made a mark on the projection of the Great Pyramid on the ground, and then measured the distance from the bottom of the Pyramid to the projection spire. In this way, he reported the exact height of the pyramid. At the request of Pharaoh, he explained how to push the principle from "shadow length equals body length" to "tower shadow equals tower height", which is today's similar triangles theorem.

Archimedes

King Shiloh of Syracuse asked the goldsmith to make a crown out of pure gold. Because it is suspected that there is silver mixed in it, Archimedes is invited to identify it. When he entered the bathtub to take a bath, the water overflowed outside the bathtub, so he realized that although the weight of objects made of different materials was the same, the discharged water would be different because of their different volumes. According to this truth, it can be judged whether the crown is adulterated.

Galois was born in a town not far from Paris. His father is the headmaster of the school and has served as mayor for many years. The influence of family makes Galois always brave and fearless. 1823, 12-year-old galois left his parents to study in Paris. Not content with boring classroom indoctrination, he went to find the most difficult mathematics original research by himself. Some teachers also helped him a lot. Teachers' evaluation of him is "only suitable for working in the frontier field of mathematics".

Von Neumann, one of the most outstanding mathematicians in the 20th century. As we all know, the electronic computer invented by 1946 has greatly promoted the progress of science and technology and social life. In view of von Neumann's key role in the invention of electronic computers, he is called "the father of computers" by westerners. From 19 1 1 to 192 1, von Neumann got ahead when he was studying in Lu Se Lun Middle School in Budapest, and was highly valued by teachers. Under the individual guidance of Mr. Fichte, von Neumann published his first mathematical paper in cooperation.

On the Discovery of Irrational Numbers

The Pythagorean school of ancient Greece believed that any number in the world could be expressed by integer or fraction, which was their creed. One day, hippasus, a member of this school, suddenly found that the diagonal of a square with a side length of 1 was a strange number, so he studied hard and finally proved that it could not be expressed by integers or fractions. But it broke the Pythagorean creed. So Pythagoras ordered him not to reveal it. But Siberus revealed the secret. Pythagoras was furious and wanted to put him to death Siberus ran away at once, but he was caught and thrown into the sea, giving his precious life for the development of science. The numbers discovered by Siberus are called irrational numbers. The discovery of irrational numbers led to the first mathematical crisis and made great contributions to the development of mathematics.

history of chinese mathematics

Mathematics is an important subject in ancient science in China. According to the characteristics of the development of ancient mathematics in China, it can be divided into five periods: the germination period; The formation of the system; Development; Prosperity and the integration of Chinese and western mathematics.

The Germination of Ancient Mathematics in China

At the end of primitive commune, after the emergence of private ownership and commodity exchange, the concepts of number and shape developed further. The pottery unearthed during Yangshao culture period has been engraved with the symbol representing 1234. By the end of the primitive commune, written symbols had begun to replace knotted notes.

Pottery unearthed in Xi 'an Banpo has an equilateral triangle with 1 ~ 8 dots and a square pattern with 100 small squares. The houses in Banpo site are all round and square. In order to draw circles and determine straightness, people have also created drawing and measuring tools such as rulers, moments, rulers and ropes. According to Records of Historical Records Xia Benji, Yu Xia used these tools in water conservancy.

In the middle of Shang Dynasty, a set of decimal numbers and notation had been produced in Oracle Bone Inscriptions, the largest of which was 30 thousand; At the same time, the Yin people recorded the date of 60 days with 60 names, including Jiazi, Yechou, Bingyin and Dingmao, which were composed of ten heavenly stems and twelve earthly branches. In the Zhou Dynasty, eight kinds of things were previously represented by eight diagrams composed of yin and yang symbols, which developed into sixty-four hexagrams, representing sixty-four kinds of things.

The book Parallel Computation in 1 century BC mentioned the methods of using moments of high, deep, wide and distance in the early Western Zhou Dynasty, and listed some examples, such as hook three, strand four, chord five and ring moments can be circles. It is mentioned in the Book of Rites that the aristocratic children of the Western Zhou Dynasty have to learn numbers and counting methods since they were nine years old, and they have to be trained in rites and music, shooting, controlling, writing and counting. As one of the "six arts", number has begun to become a special course.

During the Spring and Autumn Period and the Warring States Period, calculation has been widely used and decimal notation has been used, which is of epoch-making significance to the development of mathematics in the world. During this period, econometrics was widely used in production, and mathematics was improved accordingly.

The contention of a hundred schools of thought in the Warring States period also promoted the development of mathematics, especially the dispute of rectifying the name and some propositions were directly related to mathematics. Famous scholars believe that the abstract concept of a noun is different from its original entity. They put forward that "if the moment is not square, the rules cannot be round", and defined "freshman" (infinity) as "nothing outside the big" and "junior" (infinitesimal) as "nothing inside the small". He also put forward such propositions as "a foot away, within half a day, inexhaustible".

Mohism believes that names come from things, and names can reflect things from different sides and depths. Mohist school gave some mathematical definitions. Such as circle, square, flat, straight, sub (tangent), end (point) and so on.

Mohism disagreed with the proposition of "one foot" and put forward the proposition of "non-half" to refute: if a line segment is divided into two halves indefinitely, there will be a non-half, which is a point.

The famous scholar's proposition discusses that a finite length can be divided into an infinite sequence, while the Mohist proposition points out the changes and results of this infinite division. The discussion on the definition and proposition of mathematics by famous scholars and Mohists is of great significance to the development of China's ancient mathematical theory.

The Formation of Ancient Mathematics System in China

Qin and Han dynasties were the rising period of feudal society, with rapid economic and cultural development. The ancient mathematical system of China was formed in this period, and its main symbol was that arithmetic became a specialized subject, and the emergence of mathematical works represented by Nine Chapters of Arithmetic.

Nine Chapters Arithmetic is a summary of the development of mathematics during the establishment and consolidation of feudal society in the Warring States, Qin and Han Dynasties. As far as its mathematical achievements are concerned, it is a world-famous mathematical work. For example, the operation of quartering, the present skills (called the three-rate method in the west), square roots and square roots (including the numerical solution of quadratic equations), the skills of surplus and deficiency (called the double solution in the west), various formulas of area and volume, the solution of linear equations, the principle of addition and subtraction of positive and negative numbers, the Pythagorean solution (especially the Pythagorean theorem and the method of finding Pythagorean numbers) and so on are all very high levels. Among them, the solution of equations and the addition and subtraction of positive and negative numbers are far ahead in the development of mathematics in the world. As far as its characteristics are concerned, it forms an independent system centered on calculation, which is completely different from ancient Greek mathematics.

"Nine Chapters Arithmetic" has several remarkable characteristics: it adopts the form of mathematical problem sets divided into chapters according to categories; Formulas are all developed from counting method; Mainly arithmetic and algebra, rarely involving graphic properties; Attach importance to application and lack of theoretical explanation.

These characteristics are closely related to the social conditions and academic thoughts at that time. In Qin and Han dynasties, all science and technology should serve the establishment and consolidation of feudal system and the development of social production at that time, emphasizing the application of mathematics. Nine Chapters of Arithmetic, which was finally written in the early years of the Eastern Han Dynasty, ruled out the discussion of famous scholars and Mohists in the Warring States period on the definition and logic of nouns, but focused on mathematical problems and their solutions closely combined with production and life at that time, which was completely consistent with the development of society at that time.

Mathematics that exists everywhere in life.

The world is full of wonders, and there are many interesting things in our mathematics kingdom. For example, in my ninth exercise book, there is a thinking question that reads: "A bus goes from Dongcheng to Xicheng at a speed of 45 kilometers per hour and stops after 2.5 hours. At this time, it is just 18 km away from the center of the east and west cities. How many kilometers is it between East and West? When Wang Xing and Xiaoying solve the above problems, their calculation methods and results are different. Wang Xing's mileage is less than Xiao Ying's, but xu teacher said that both of them were right. Why is this? Have you figured it out? You can also calculate the calculation results of both of them. " In fact, we can quickly work out a method for this problem, which is: 45× 2.5 = 1 12.5 (km),112.5+18 =130.5 (. In fact, we have neglected a very important condition here, that is, the word "Li" mentioned in the condition is "just 18 km from the center of the east and west cities", and it does not say whether it has not yet reached the midpoint or exceeded the midpoint. If the distance from the midpoint is less than 18km, the formula is the previous one; If it is greater than 18km, the formula should be 45× 2.5 = 1 12.5 (km), 1 12.5-65448. Therefore, the correct answer should be: 45 × 2.5 = 1 12.5 (km),12.5+18 =130.5 (km),/kloc-. Two answers, that is to say, Wang Xing's answer and Xiaoying's answer are comprehensive.

In daily study, there are often many math problems with multiple solutions, which are easily overlooked in practice or examination. This requires us to carefully examine the problem, awaken our own life experience, scrutinize it carefully, and fully and correctly understand the meaning of the problem. Otherwise, it is easy to ignore other answers and make a mistake of generalizing.

Interesting math topic

1. Using the total number 1, 2 * * can discharge four double digits 1 1,12,22,21.

2. Use 1, 2, 3, and a total of * * * can discharge _ _ 27 _ _ three digits.

3. With the four numbers 1, 2, 3 and 4, a total of * * * can discharge _ _ 4 4 _ _ 4 digits.

4. The lock core of domestic marble lock consists of five metal cylindrical bars with different lengths. How can I ask: Among the door locks made of this metal cylindrical bar, there are _ _ 5 5 _ _ locks that do not have the same key.

5. If the lock core is composed of 10 metal cylinders with different lengths, then there are _ _10/0 _ _ locks without the same key.

Observe the following groups of formulas, explore their laws, and express your findings with formulas containing 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 _ _ _ _ _ _ _ _ _ _

As shown in the figure, in quadrilateral ABCD, ∠ bad = 60, ∠ b = ∠ d = 90, BC= 1 1, and CD=2, find the length of diagonal AC.

∠CAD=β，∠CAB=60 -β

DC/AC=sinβ，BC/AC=sin∠CAB=sin(60 -β)

Ac = DC/sinβ = BC/sin (60-β) is substituted into BC = 1 1, and CD = 2.

The general score (sub) is 22/11sinβ = 22/2sin (60-β).

1 1 sinβ= 2 sin(60-β)=√3 cosβ-sinβ

Tanβ=√3/ 12，CD=2，AD=8√3。

AC= 14 is obtained from Pythagorean theorem.

Give points for writing so hard.

Respondents: unknown passers-by-level 1: 20 10-8-22: 2 1: 02.