In a few words, three long and two short, three transgressions and five times, three or five groups, half-hearted, three feet in the air.
Split, cosmopolitan, extending in all directions, in all directions.
Colorful, colorful, colorful, colorful, colorful.
All six vital organs have lost their functions ― they are at a loss/numb.
Fragmented, patchwork, too many cooks, conflicting views.
Support from all directions, eight immortals crossing the sea
Nine cows and two tigers, nine Niu Yi hairs, a narrow escape, cloud nine.
Heinous, perfect and urgent.
Geometric series, a story about mathematical knowledge: a series starts from the second term, and the ratio of each term to the previous term is the same constant, so it is called geometric series, Changshu is called common ratio, and geometric series is also called geometric series. It was written in China's ten volumes of The Art of War, A Brief Introduction, from 67 to 270 AD. The most interesting story is the story of King Shehan of India. It is said that Sass Ban, the prime minister of She Hanwang, invented chess. She Hanwang liked it very much and decided to let Sasban ask for the reward he wanted. Sass Ban asked to give him only some wheat, according to his method. His method is to put a grain of rice in the first grid, double the first grid, and proceed to the 64th grid in turn. How did she Hanwang realize that the sum of geometric series is increasing at what speed? According to our current knowledge, S = 264-1/2-1= 264-1. If one liter of wheat is calculated as 150000 grains, it is about 140 trillion liters of wheat. According to the current average output, it is about the average output of the world for more than 1000 years.
Collect idioms related to birds. Birds fly to the phoenix, stupid birds fly first, Can Cong birds fly first, with a long-necked beak.
Fish in the pond, birds in cages, birds in snakes, birds in the sky, birds in the sky, turtles and birds in the sky.
A bird with a cold face, a bird with a sweet face, a bird with a frightened voice and a tired bird all know it.
A frightened bird, a bird covered with eggs, a bird in a flying cage, a bird in an ape cage, a bird in a pond and a fish in a cage.
A bird hides its path with dead wood, a bird hides its beast with a narrow intestine, and a poor bird covers its dangerous nest with white.
Birds burn fish, rotten birds, leather, birds, scary mice, birds, traces of insects, birds are all hidden.
Birds get together to get scales, birds startle mice, birds startle fish, birds startle fish, and birds break up fish.
Birds cry, apes cry, birds face, mandarin fish-shaped shotguns for guns, shotguns for guns, poor birds peck.
Birds enter the cage, birds and beasts scatter birds, birds and beasts scatter fish, birds crow and flowers fall.
Collecting fairy tales related to magpies The Magpie Bridge is a bridge built by magpies in ancient Han folk love stories. According to legend, the Cowherd and the Weaver Maid are separated by the Milky Way and can only meet on the seventh day of the seventh lunar month. In order to meet the Cowherd and the Weaver Girl, magpies from all over the world will fly over and use their bodies to get close to each other and build a bridge. This bridge is called Magpie Bridge. Cowherd and Weaver Girl meet on this magpie bridge.
People regard magpies as a symbol of "good luck". There are many beautiful myths and legends about it. Legend has it that magpies can bring good news. There is a story that there was a man named Li Jingyi in the last years of Zhenguan. There is a magpie nest in the tree in front of his house. He often feeds the magpies in the nest. For a long time, people and birds have feelings. On one occasion, Li Jingyi was wrongly imprisoned, which made him feel painful. Suddenly one day, the bird he fed stopped at the prison window and kept barking. He thought there would be good news. Sure enough, he was acquitted three days later. It's because magpies become people and falsely preach the imperial edict. These stories prove that the custom of drawing magpies for good luck is very popular, and there are many kinds: for example, two magpies face to face, which is called "greeting"; Double magpies add an ancient coin called "happiness is in sight"; A badger and a magpie looked at each other under the tree and shouted "Happy". The most popular picture is the picture of a magpie climbing a plum branch to report good news, which is also called "beaming"
Collect stories related to self-esteem and self-confidence (1) and recommend yourself.
During the Warring States period, the Qin army surrounded Handan, the capital of Zhao. Zhao sent to Chu for help. Diners in Ping Yuanjun are very confident, recommend themselves and ask to go. As a result, he finally persuaded the king of Chu to agree to rescue Zhao. Later generations used "volunteer" to describe volunteer service and self-recommendation. This story also reflects that Mao Sui is a confident person.
(2) Yan Zili Chu.
During the Spring and Autumn Period, Qi and Chu were both big countries. On one occasion, the King of Qi sent a doctor, Yan Zi, to Chu. Relying on the strength of his own country, the king of Chu wanted to take the opportunity to insult Yan Zi and show the prestige of Chu State. Knowing that Yan Zi was short, the King of Chu dug a hole five feet high beside the city gate. When Yan Zi came to the State of Chu, the King of Chu told people to close the city gate and let Yan Zi out of this hole. Yan Zi looked at it and said to the receptionist, "This is a dog hole, not a city gate. Only by visiting the' Dog Country' can you enter from the dog hole. " I'll wait here for a while, and you'll find out what kind of country Chu is. "The receptionist immediately told this to the king of Chu. The king of Chu had to ask him to open the city gate and welcome Yan Zi in.
(3) latitude and longitude reclamation
After Emperor Yan's daughter drowned in the East China Sea, her soul became a bird named Jingwei. Although small, Jingwei is full of confidence in the face of the vast sea. He often takes wood and stones from Xishan to fill the East China Sea, vowing to fill it up.
I learned a lot from the related idiom story 1. Explanation: it means that you have gained a lot in thought/form. Bandit: Yes or No? 2, fruitful explanation: fruitful, big fruit. Accumulate a lot. Describe a lot of gains. It is also a metaphor for great achievements. 3, full mouth explanation: full mouth back. Describe a bumper harvest.
A story about mathematicians' mathematical knowledge (1) Cardinality of Cantor continuum.
1874, Cantor speculated that there was no other cardinality between countable set cardinality and real set cardinality, that is, the famous continuum hypothesis. 1938, Austrian mathematical logician Godel, who lived in the United States, proved that there is no contradiction between the continuum hypothesis and the axiomatic system of ZF set theory. 1963, American mathematician P.Choen proved that the continuum hypothesis and ZF axiom are independent of each other. Therefore, the continuum hypothesis cannot be proved by ZF axiom. In this sense, the problem has been solved.
(2) Arithmetic axiom system is not contradictory.
The contradiction of Euclidean geometry can be summed up as the contradiction of arithmetic axioms. Hilbert once put forward the method of proving formalism plan, but Godel's incompleteness theorem published in 193 1 denied it. Gnc(G. genta en,1909-1945)1936 proved the non-contradiction of the arithmetic axiomatic system by means of transfinite induction.
(3) It is impossible to prove that two tetrahedrons with equal base and equal height are equal in volume only according to the contract axiom.
The significance of the problem is that there are two tetrahedrons with equal height, which cannot be decomposed into finite small tetrahedrons, so that the congruence of the two tetrahedrons (M. DEHN) has been solved in 1900.
(4) Take a straight line as the shortest distance between two points.
This question is rather general. There are many geometries that satisfy this property, so some restrictions are required. 1973, the Soviet mathematician Bo gref announced that this problem was solved under the condition of symmetrical distance.
(5) Conditions for topology to be a Lie group (topological group).
This problem is simply called the analytic property of continuous groups, that is, whether every regional Euclidean group must be a Lie group. 1952 was solved by Gleason, Montgomery and Zipin. 1953, Hidehiko Yamanaka of Japan got a completely positive result.
(6) Axiomatization of physics, which plays an important role in mathematics.
1933, the Soviet mathematician Andrei Andrey Kolmogorov axiomatized probability theory. Later, he succeeded in quantum mechanics and quantum field theory. However, many people have doubts about whether all branches of physics can be fully axiomatized.
(7) Proof of transcendence of some numbers.
It is proved that if α is algebraic number and β is algebraic number of irrational number, then α β must be transcendental number or at least irrational number (for example, 2√2 and eπ). Gelfond of the Soviet Union (1929) and Schneider and Siegel of Germany (1935) independently proved its correctness. But the theory of transcendental number is far from complete. At present, there is no unified method to determine whether a given number exceeds the number.
(8) The distribution of prime numbers, especially for Riemann conjecture, Goldbach conjecture and twin prime numbers.
Prime number is a very old research field. Hilbert mentioned Riemann conjecture, Goldbach conjecture and twin prime numbers here. Riemann conjecture is still unsolved. Goldbach conjecture and twin prime numbers have not been finally solved, and the best result belongs to China mathematician Chen Jingrun.
(9) Proof of the general law of reciprocity in arbitrary number field.
192 1 was basically solved by Kenji Takagi of Japan, and 1927 was basically solved by E.Artin of Germany. However, category theory is still developing.
(10) Can we judge whether an indefinite equation has a rational integer solution by finite steps?
Finding the integer root of the integral coefficient equation is called Diophantine (about 2 10-290, an ancient Greek mathematician) equation solvable. Around 1950, American mathematicians such as Davis, Putnam and Robinson made key breakthroughs. In 1970, Baker and Feros made positive conclusions about the equation with two unknowns. 1970. The Soviet mathematician Marty Sevic finally proved that, on the whole, the answer is negative. Although the result is negative, it has produced a series of valuable by-products, many of which are closely related to computer science.
Quadratic theory in (1 1) algebraic number field.
German mathematicians Hassel and Siegel made important achievements in the 1920s. In 1960s, French mathematician A.Weil made new progress.
Composition of (12) class domain.
That is, Kroneck's theorem on Abelian field is extended to any algebraic rational field. This problem has only some sporadic results and is far from being completely solved.
The impossibility of (13) combination of binary continuous functions to solve the seventh general algebraic equation.
The root of equation x7+ax3+bx2+cx+ 1=0 depends on three independent variables A, B and C; X=x(a, b, c). Can this function be represented by a binary function? This problem is about to be solved. 1957, the Soviet mathematician Arnold proved that any continuous real function f(x 1, x2, x3) on [0, 1] can be written as ∑ hi (ξi (x 1, x2), x3). Andre Andrey Kolmogorov proved that f(x 1, x2, x3) can be written as ∑ hi (ξ I1(x1)+ξ I2 (x2)+ξ i3 (x3)) (I =/kloc-0). In 1964, Vituskin is extended to the case of continuously differentiable, but the case of analytic function is not solved.
The finite proof of (14) some complete function systems.
That is, the ring formed by polynomial fi(i= 1, …, m) with x 1, X2, Xn as independent variables on the field k, where r is k, Japanese mathematician Masayoshi Nagata gave a negative solution to this problem related to algebraic invariants in 1959 with a beautiful counterexample.
(15) Establish the foundation of algebraic geometry.
Dutch mathematicians Vander Waals Deng 1938 to 1940 and Wei Yi 1950 have solved the problem.
(15) Note 1 The strict foundation of Schubert counting calculus.
A typical problem is that there are four straight lines in three-dimensional space. How many straight lines can intersect all four? Schubert gave an intuitive solution. Hilbert asked to generalize the problem and give a strict basis. Now there are some computable methods, which are closely related to algebraic geometry. But the strict foundation has not been established.
Topological research on (16) algebraic curves and surfaces.
The first half of this problem involves the maximum number of closed bifurcation curves in algebraic curves. In the second half, it is required to discuss the maximum number N(n) and relative position of limit cycles of dx/dy=Y/X, where x and y are polynomials of degree n of x and y. For the case of n=2 (i.e. quadratic system), 1934, Froxianer obtains n (2) ≥1; 1952, Bao Ting got n (2) ≥ 3; 1955, Podlovschi of the Soviet Union declared that n(2)≤3, which was the result of a shock for a while, but was questioned because some lemmas were rejected. Regarding the relative position, China mathematician and Ye proved in 1957 that (E2) does not exceed two strings. 1957, China mathematicians Qin Yuanxun and Pu Fujin illustrate that the equation with n = 2 has at least three series limit cycles. In 1978, under the guidance of Qin Yuanxun and Hua, Shi Songling and Wang of China respectively gave at least four concrete examples of limit cycles. In 1983, Qin Yuanxun further proved that the quadratic system has at most four limit cycles, and the structure is (1 3), thus finally solving the structural problem of the solution of the quadratic differential equation and providing a new way for studying the Hilbert problem (16).
The square sum representation of (17) semi-positive definite form.
The rational function f (x 1, ..., xn) is for any array (x 1, ..., xn). Are you sure that f can be written as the sum of squares of rational functions? 1927 Atin has been definitely solved.
(18) Construct space with congruent polyhedron.
German mathematicians Bieber Bach (19 10) and Reinhardt (1928) gave some answers.
(19) Is the solution of the regular variational problem always an analytic function?
German mathematician Berndt (1929) and Soviet mathematician Petrovsky (1939) have solved this problem.
(20) Study the general boundary value problem.
This problem is progressing rapidly and has become a major branch of mathematics. I was still researching and developing a few days ago.
(2 1) Proof of the existence of solutions for Fuchs-like linear differential equations with given singularities and single-valued groups.
This problem belongs to the large-scale theory of linear ordinary differential equations. Hilbert himself obtained important results in 1905 and H.Rohrl in 1957 respectively. Deligne, a French mathematician from 65438 to 0970, made outstanding contributions.
(22) Analytic function is a single-valued function with automorphism function.
This problem involves the difficult Riemann surface theory. In 1907, P.Koebe solved a variant and made an important breakthrough in the study of this problem. Other aspects have not been solved.
(23) Carry out the research of variational method.
This is not a clear mathematical problem. Variational method has made great progress in the 20th century.
It can be seen that Hilbert's problem is quite difficult. It is the difficulties that attract people with lofty ideals to work hard.
Collect stories about animal idioms, etc.
A man once saw a rabbit run out on the road and suddenly hit a stump and died. The man took the rabbit home for food. After a few days, he had nothing to eat, so he stayed beside the stump every day. He was asked what he was doing. He said he would wait until the rabbit hit him before eating rabbit meat, and then he never waited for the rabbit to come.
Looking at the sky from the bottom of the well-the view is very narrow.
A frog is sitting in a well, and a bird is flying around the well.
The frog asked the bird, "Where did you fly from?"
The bird replied, "I flew from far away." I flew more than a hundred miles in the sky, and I was thirsty. I came down to find some water to drink. "
The frog said, "friend, don't talk big!" " The sky is only as big as the wellhead. Do you still need to fly that far? "
"You are mistaken," said the bird. The sky is boundless and vast! " "
The frog smiled and said, "friend, I sit in the well every day and look up at the sky." I can't make mistakes. "
The bird also smiled and said, "Friend, you are wrong. If you don't believe me, jump out of the well and have a look. "
This idiom story of "sitting on a well and watching the sky" is a household name, and it is usually used to describe someone with limited knowledge and short-sightedness; But I think this story emphasizes that people should broaden their minds and broaden their horizons at the same time, but ignores other factors and information worthy of attention. When we analyze this idiom story again, it will have more profound practical enlightenment.
Idiom stories related to numbers accomplish nothing.
Opposite the two dragons, the play is playing a ball.
With the arrival of spring, prosperity begins-the new year indicates prosperity.
Peace in the four seasons
(of a person's mental state) Like a well, seven barrels go up and eight barrels go down ―― mental instability.
Perfect in every respect/aspect.
Mathematical knowledge and story (about 30 words) One day, a grocer bought carrots and a kilo of carrots 5 yuan in the market. A man wants to buy 8 kilograms of carrots, but he doesn't know how much it costs.