Gu Sen: When we were growing up in university, we used ready-made knowledge and theorems to solve problems. Many people still don't know the formula or reason put forward by scientists after graduation. But the story behind it is actually more exciting. Including many mathematical conclusions, in fact, people's guesses may be wrong at first, or even draw completely opposite conclusions, and then gradually approach this truth. These are not in the textbook. There are many books that are purely storytelling, and the silent universe tells the origin of many mathematical formulas and their influence on human beings, which is very powerful.
I think physical formulas have a greater impact on the significance of human development. In fact, mathematical formulas are not the most meaningful things in mathematics. Mostly theorems, not what equals what.
Li miao: I think even liberal arts students need cross-border study. I strongly support the reform of college entrance examination, regardless of arts and sciences. A thousand years ago, there was no division. Under the guidance of human science, we must go back to the past after the division of labor is extremely detailed and science develops to a certain extent. Is to cross the border If you don't cross the line, your future employment opportunities and all aspects will be greatly restricted. So I am very much looking forward to seeing that the college entrance examination will no longer be divided into subjects in my lifetime.
Gu Sen: If it's for the exam, if the math exam is cancelled, will we still study? I think mathematics should be divided into two levels. One is to add, subtract, multiply and divide within 100 in primary school, and learn to settle accounts. Further solve equations, geometric conclusions, etc. , may not be used in life. It is enough to learn mathematics in the second day of junior high school, and then go up, maybe it is purely out of interest. Mathematical physics is meaningful only when you want to do something completely new in a certain professional field and benefit mankind.
Complete Mathematical Manuscripts: Behind the Great Mathematical Formulas
1971may 15, Nicaragua issued a set of ten cards entitled? Ten mathematical formulas to change the face of the world? Stamps, selected by some famous mathematicians, are commended by ten formulas that have great influence on the development of the world. These ten formulas not only benefit mankind, but also have typical mathematical beauty, that is, simplicity, harmony and strangeness.
(A) the basic law of finger counting
Stamps? 1+ 1=2? It is the first stamp in this set and the basic formula of human understanding of quantity at the beginning. Human ancestors started from this formula, piling stones, counting shells, counting branches, counting bamboo pieces, then scoring, counting knots, and then creating words, numbers, abacus, calculation, calculator and other counter tools. Everything starts with the basic law of hand index, because people have ten fingers to assist in calculation. Undoubtedly, it is this fact that naturally gave birth to the decimal system that we are familiar with now. The birth of notation and decimal system is a leap in the history of civilization.
(2) Pythagorean Theorem
If the right side of a right triangle is A and B and the hypotenuse is C, then A2+B2=C2, which is the most famous pythagorean theorem in Euclid geometry. It is widely used in mathematics and human practice. Pythagoras, a famous ancient Greek philosopher and mathematician, gave the first proof of this theorem abroad, so it is generally called? Pythagoras theorem? .
China knew it in Shang Gao's time? Hook three strands, four strings and five? Relationship, much earlier than Pythagoras, but China's proof of Pythagoras theorem is a relatively late thing, until the Three Kingdoms period, Zhao Shuangcai first proved it by area filling method. One of the great influences of Pythagoras theorem is the discovery of irrational numbers. The diagonal length of a square with a side length of 1 is 0, which cannot be expressed by integer or integer ratio, that is, fraction. Does this discovery deny the Pythagorean school? What is it? At that time, people thought that integers and fractions were easy to understand, so they were called rational numbers, but the newly discovered numbers existed although they were not easy to understand, so they were named? Irrational number? .
(3) Archimedes lever principle
The third stamp recognizes the mathematical formula F 1X 1=F2X2, where f is the acting force, x is the arm of force and FX is the moment. In principle, as long as the power arm is long enough and the resistance arm is short enough, you can pry a heavy object with a small enough force. To this end, Archimedes said an old saying:? Give me a fulcrum, I can move the earth? . Hehe, you see how confident physicists are! ! ! In addition to the lever principle, Archimedes also discovered the famous law of buoyancy and a large number of geometric theorems, and he was also one of the pioneers of calculus. By later mathematicians? God of mathematics? Among the three most important mathematicians in human history, Archimedes is the first, and the other two are Newton and Gauss respectively.
Napier exponent and logarithmic formula
The logarithmic relationship is Napier formula, where e=2.7 1828. The inventor of logarithm is Baron Napier, an amateur mathematician in Scotland. From the age of 44, after 20 years of research on large number calculation technology, he finally invented logarithm independently. In 2004,1665438+in 2004, he published his masterpiece "The Wonderful Law of Logarithms", and the amazing invention of logarithmic tables quickly spread throughout the European continent. Galileo made a grand speech: Give me time, space and logarithm, and I can create a universe. ? Logarithmic tables have been widely used by mathematicians, accountants, navigators and scientists for centuries. Logarithm and exponent have become the essence of mathematics, which is what every middle school student must learn.
(5) Newton's law of universal gravitation
The fifth stamp immediately reminds people of the well-known story of Newton and Apple. In that magical festival, an apple accidentally fell from the tree, which was a turning point in the history of human thought. It opened the minds of people sitting in the garden, and finally Newton discovered the epoch-making law of gravity for mankind.
Where g is the gravitational constant, m 1 and m2 respectively represent the mass of two objects, and r is the distance between two objects.
(6) Maxwell electromagnetic equation
The sixth formula is Maxwell's electromagnetic equations, which determines the universal relationship among charge, current, electric field and magnetic field, and is the basic equation of electromagnetism. Maxwell's equations show that as long as there is a changing magnetic field somewhere in space, the eddy electric field can be excited, and the alternating electric field and the magnetic field can excite each other to form a continuous electromagnetic oscillation, that is, electromagnetic waves. This formula can prove that the propagation speed of electromagnetic wave in vacuum is equal to that of light in vacuum, which is not accidental coincidence, but because light is an electromagnetic wave with a certain wavelength, which is Maxwell's electromagnetic theory of light. Maxwell is another great physicist who integrated electromagnetism after Faraday. The theory of electromagnetism has laid the foundation of modern electric power industry, electronic industry and radio industry. 187 1 was employed as a professor of experimental physics at Cambridge University in charge of establishing the first physics laboratory in the university? Cavendish laboratory.
(7) Einstein's mass-energy relationship
E=mc2
Where c is the speed of light, m is mass and e is energy. This is the most famous mass-energy relationship later. This is the theoretical basis for making atomic bombs. 1905 The person who put forward this formula is Einstein, a 26-year-old employee of Bern Patent Office. 19 15 established the general theory of relativity and determined the relationship between space, time and matter. Mass-energy conversion formula and relativity have great influence. Nowadays, nuclear energy is widely used in agriculture and military affairs, and black holes, time travel and space bending all originate from relativity. Einstein began to learn the violin at the age of six and stayed with him all his life. Art improved his aesthetic ability, and he also pursued the beauty of mathematics (simplicity and symmetry) in physics all his life.
(VIII) De Broglie formula
The formula for commending the eighth stamp is De Broglie's formula for wave-particle duality proposed in 1924:? =h/mv，
Among them? Is the wavelength of the matter wave related to the particle, H is Planck constant, and mv is the momentum of the particle. Before de Broglie, people's understanding of nature was limited to two basic material types: physical objects and fields. De Broglie originally studied history, but influenced by the mathematician Poincare, he changed to science. 1924, he put forward the concept of "matter wave" in his doctoral thesis, which caused a sensation all over the world. He thinks that any object and particle have the properties of wave and particle at the same time, and uses Einstein's theory of relativity to derive the formula of material wave wavelength. His view was later confirmed by Davidson's experiment. The concept of matter wave also provides an important theoretical basis for the development of wave mechanics.
(9) Boltzmann formula
1854, clausius, a german scientist, first introduced the concept of entropy, which is a quantity indicating the disorder degree of closed systems. Change? The meaning of. This quantity will not change in the reversible process, but will become larger in the irreversible process. Like a lazy man's room, if no one helps him clean it, the room will only go down in chaos and never become neat. Living things can't live without it? Law of entropy increase? Organisms need to absorb negative entropy from the outside to offset the increase of entropy. In 1877, Boltzmann expressed the disorder degree of the system with the following relation: S=kLnW, where k is Boltzmann constant and s is the entropy value of the macro system, which is a measure of the degree of molecular movement or disorder. W is the number of possible microstates. The bigger w is, the more chaotic the system is. From this, we can see the microscopic significance of entropy: entropy is a measure of the disorder of molecular thermal motion in the system. Because of his novel viewpoint, it was not accepted by many famous scholars at first, and Boltzmann paid a huge price for it, which became an important reason for his personal tragedy (suicide). The formula S=kLnW was engraved on Boltzmann's tombstone in recognition of his great originality.
(10) Tsiolkovsky formula
In the Goddess Chang'e flying to the moon, thousands of families are flying, and human beings have been longing for space for a long time and have made unremitting efforts for it. The key to conquering space is rocket technology.
When it comes to modern rockets, we have to mention tsiolkovsky, the world-recognized pioneer of space theory. It was he who put forward the possibility of using rockets for interstellar navigation and launching satellites. The relationship between rocket structural characteristics and flight speed is established, that is, the famous Tsiolkovsky formula. Where V is the speed increment of the rocket, Ve is the speed of the jet relative to the rocket, and m0 and mi represent the mass of the rocket when the engine is turned on and off, respectively. It has become the key to human conquest of space.
1957, the Soviet Union launched the first artificial satellite, which started the space age. 196 1 year, it sent its first astronaut, Gagarin, and won the first battle of the space race. 1969, the United States sent Armstrong to the moon. Tsiolkovsky focused on ancient rocket technology in China, and asked people to translate military works in the late Ming and early Qing dynasties for reference, especially interested in Wu Beizhi. At that time, there were nearly 30 kinds of military rockets in China. God machine fire dragon arrow? Or? Fire dragon out of the water? Weapons like this fascinated him, and he had more dreams and inspirations, and soon wrote a book, Dreams of Heaven and Earth. He has a very incisive famous saying: the earth is the cradle of human beings, but people can't live in the cradle forever. ?
Complete works of mathematical manuscripts: famous mathematical sayings
1, mathematics is the queen of science and number theory is the queen of mathematics. Gauss
The scientific level of a country can be measured by the mathematics it consumes.
Number theory is the oldest branch of human knowledge. However, some secrets in his heart are closely related to his most ordinary truth. Smith (last name)
4. Read Euler, read Euler, he is our teacher. Laplace (Marquis)
Sometimes, you can't get the simplest and most wonderful proof at first, but it is this kind of proof that can go deep into the wonderful connection of higher arithmetic truth. This is the motivation for us to continue our research, which can make us find something most. Gauss
6, a science, only the successful use of mathematics, can achieve a truly perfect level. Marx
7. I am determined to let go of the only abstract geometry. In other words, stop thinking about problems that are only used to practice ideas. I did this to study another kind of geometry, that is, Cartesian geometry, which aims to explain natural phenomena.
8. A mathematician who is not a poet can never be a complete mathematician, Wilstrass.
9. Pure mathematics, in its modern development stage, can be said to be the most primitive creation of human spirit. Huaidehai
We can expect that with the development of education and entertainment, more people will like music and painting. However, few people can really appreciate mathematics. bell
1 1, "The problem is the heart of mathematics. Plhal Moss
12, this is a reliable law. When the author of mathematics or philosophy works writes in vague and abstruse words, he is talking nonsense. Answer? n？ Huaidehai
13. As long as a branch of science can ask too many questions, it is full of vitality, while no questions indicate the termination or decline of independent development. Hilbert
14, pure mathematics, in its modern development stage, can be said to be the most primitive creation of human spirit. Huaidehai
15, the number is not intuitive when it is invisible, and it is difficult to be nuanced when it is small. Numbers and shapes are interdependent. How can we divide them into two sides? Hua
16, a strange beauty rules the kingdom of mathematics, which is not as similar as artistic beauty and natural beauty, but it deeply infects people's hearts and arouses people's appreciation of her, which is very similar to artistic beauty, Cuomo.
17, an unshakable cornerstone of mathematical science and a rich source of promoting human progress.
18, although we are not allowed to see through the secrets of nature and know the real reason of the phenomenon, it is still possible that the necessary fictional assumptions are enough to explain many phenomena. Euler provenance
19. The problem is the core of mathematics. Plhal Moss
20. No problem can touch people's emotions as deeply as infinity, and few other concepts can stimulate reason to produce rich ideas as infinity, but no other concepts can be clarified as infinity. Hilbert
2 1, what is a masterpiece, extraordinary! Galois
22. We appreciate mathematics, and we need it. Chen shengshen
23, mathematics is a deductive knowledge, starting from a set of postulates, through logical reasoning, draw a conclusion. Chen shengshen
24. Mathematicians are actually fascinated. Without infatuation, there would be no math Novalis.
25. The incomparable eternity and omnipotence of mathematics and its independent effect on time and cultural background are the direct consequences of its essence. Answer? Ebou
In the world of mathematics, what matters is not what we know, but how we know what Pythagoras is.
28. Simple combinations of integers have been the source of new students in mathematics for centuries. GD boekhoff (sad net name)
In the field of mathematics, the art of asking questions is more important than the art of answering questions.
30. Arithmetic is the oldest and perhaps the oldest branch of human knowledge. However, some of its deepest secrets are closely related to its most common truth.
Complete Works of Mathematical Manuscripts: 1-6 Formula
1, per share? Number of copies = total number
Total? Number of copies = number of copies
Total? Number of copies = number of copies
Multiply of 2.65438 +0? Multiple = multiple
How many times? 1 multiple = multiple
How many times? Multiplication = 1 multiplication
3. speed Time = distance
Distance? Speed = time
Distance? Time = speed
4. Unit price? Quantity = total price
Total price? Unit price = quantity
Total price? Quantity = unit price
5. Work efficiency? Working hours = total amount of work
Total amount of work? Working efficiency = working hours
Total amount of work? Working hours = working efficiency
6. Appendix+Appendix = Total
And-one addend = another addend
7. Negative-negative = difference
Negative difference = negative
Difference+Minus = Minus
8. Factor? Factor = product
Product? One factor = another factor
9. Dividends? Divider = quotient
Dividend? Quotient = divisor
Business? Divider = dividend
Calculation formula of mathematical graphics in primary schools
1, squared
Perimeter area side length
Perimeter = side length? four
C=4a
Area = side length? Length of side
S=a？ a
2. Cubic
Volume a: edge length
Surface area = side length? Side length? six
S table =a? Answer? six
Volume = side length? Side length? edge
V=a？ Answer? a
3. rectangular
Perimeter area side length
Circumference = (length+width)? 2
C=2(a+b)
Area = length? extensive
S=ab
4. Cuboid
V: volume s: area a: length b: width h: height.
(1) surface area = (length? Width+length? Height+width? High)? 2
S=2(ab+ah+bh)
(2) Volume = length? Wide? high
V=abh
5. Triangle
S area a bottom h height
Area = bottom? Tall? 2
S = huh? 2
Height of triangle = area? 2? bottom
Triangle base = area? 2? high
6. Parallelogram
S area a bottom h height
Area = bottom? high
S = ah
7. trapezoidal
Height of upper bottom b and lower bottom h in s area a
Area = (upper bottom+lower bottom)? Tall? 2
s=(a+b)？ h？ 2
8 laps
S area c circumference? D= diameter r= radius
(1) circumference = diameter =2? radius
C=？ d=2？ r
(2) Area = radius? radius
9. Cylinder
V: volume h: height s; Bottom area r: bottom radius c: bottom perimeter
(1) lateral area = bottom circumference? high
(2) Surface area = lateral area+bottom area? 2
(3) Volume = bottom area? high
(4) Volume = lateral area? 2? radius
10, conical
V: volume h: height s; Bottom area r: bottom radius
Volume = bottom area? Tall? three
Formula of sum and difference problem;
Total? Total number of copies = average
(sum+difference)? 2= large quantity
(sum and difference)? 2= decimal
And folding problems.
And then what? (multiple-1)= decimal
Decimal? Multiple = large number
(or sum-decimal = large number)
Difference problem
Poor? (multiple-1)= decimal
Decimal? Multiple = large number
(or decimal+difference = large number)
Tree planting problem:
1. The problem of planting trees on unclosed lines can be mainly divided into the following three situations:
(1) If trees are planted at both ends of the non-closed line, then:
Number of plants = number of nodes+1= total length? Plant spacing-1
Total length = plant spacing? (number of plants-1)
Plant spacing = total length? (number of plants-1)
2 If you want to plant trees at one end of the unclosed line and not at the other end, then:
Number of plants = number of nodes = total length? vertical spacing
Total length = plant spacing? Plant quantity
Plant spacing = total length? Plant quantity
(3) If no trees are planted at both ends of the non-closed line, then:
Number of plants = number of nodes-1= full 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 planting trees on the closed line is as follows
Number of plants = number of nodes = total length? vertical spacing
Total length = plant spacing? Plant quantity
Plant spacing = total length? Plant quantity
Profit and loss issues:
(profit+loss)? Difference between two distributions = number of copies participating in the distribution
(Daying-Xiaoying)? Difference between two distributions = number of copies participating in the distribution
(big loss-small loss)? Difference between two distributions = number of copies participating in the distribution
Encountered problems:
Meeting distance = speed and? Meeting time
Meeting time = meeting distance? Speed sum
Speed sum = meeting distance? Meeting time
Follow up questions:
Chasing distance = speed difference? Catch up with time
Catch-up time = catch-up distance? speed difference
Speed difference = catching distance? Catch up with time
Tap water problem:
Downstream velocity = still water velocity+current velocity
Countercurrent velocity = still water velocity-current velocity
Still water velocity = (downstream velocity+countercurrent velocity)? 2
Water velocity = (downstream velocity-countercurrent velocity)? 2
Centralized question:
Solute weight+solvent weight = solution weight.
The weight of solute? The weight of the solution? 100%= concentration
The weight of the solution? Concentration = weight of solute
The weight of solute? Concentration = solution weight
Profit and discount issues:
Profit = selling price-cost
Profit rate = profit? Cost? 100%= (price? Cost-1)? 100%
Upper and lower amount = principal? Percentage of increase and decrease
Discount = actual selling price? Original price? 100% (discount
Interest = principal? Interest rate? time