Biological research study report
Higher level mathematics research study group
"Practice tests the truth." This is the famous saying of Deng Xiaoping, the chief architect of the great reform and opening up. The mathematics in life embodies the practicality of the basic discipline of mathematics. It is the origin of life, the mathematics in life. From the market, between the buyers and sellers, to the construction of a skyscraper, the wonders of the world. All the famous works of the masters of art, all use mathematics. Similarly, there is a great connection between mathematics and various disciplines. Physics, chemistry, and even Chinese. In the creation of literature, the use of some mathematical things will make the works more philosophical.
What is mathematical beauty? This sounds like a subjective and arbitrary question. In fact, the mathematical theory itself is peculiar, subtle, concise and powerful. The creative thinking of human beings when establishing these theories is the beauty of mathematics. A correct mathematical theory reflects the objective things. Essence and law, this is the truth of mathematics; no matter how far away from reality, mathematical theory can always find its practical use and reflect its value orientation for human service. This is the goodness of mathematics. When people talk about humanistic spirit Often, the humanistic spirit is positioned at the highest level of pursuing "truth, goodness, beauty" and the comprehensive and free development of human beings. Mathematics is the unity of truth, goodness and beauty.
All along, mathematics gives our students the feeling that it is a headache, a strange symbol, an abstract concept that makes people look annoyed. If the sentence is not read, the symbol is not known, and where is the aesthetic taste. There is a song on the tracing copybook used by primary school students in China:
One two three four five, Jinmu water fire soil.
Heaven and earth are divided, the sun and the moon are the same.
In just 20 words, it contains extremely rich content. One two three four five is the smallest natural number. On the one hand, it is like the "rejuvenation" of poetry, it has a total effect, on the other hand. Refers to all quantitative relationships. Jinmu Shuihuo is the basic element that the ancients believed to constitute the material world, representing the material world. The ancients also used some natural numbers to correspond to it. The third sentence describes the vastness of the universe, and the fourth sentence describes the eternal time. It can be seen that in this short 20-word song, the quantity, the material, the time and the space are all linked together, the colorful and material world, the vast and magical space, the colorful, the beautiful, all unified in quantity. In the middle, look at the following:
a frog with a mouth,
Two eyes, four legs,
Ploped into the water.
For example, a frog corresponds to a mouth, from which there is a mapping knowledge about mathematics, which has one-to-one knowledge; and so on, two frogs have two mouths. Also, the eyes of the frog and Legs, you can apply the algebra knowledge of multiplication. A frog has two eyes, four legs, then, n frogs have 2n eyes, 4n legs.
Su Shi, a writer of the Song Dynasty, not only wrote poems well, but also made calligraphy paintings. At one time, he painted a picture of "Hundred Birds Returning to the Nest", a champion named Lun Wenxu in Guangdong, in his Painting a poem:
Returning one more one, three four five six seven eight.
How many birds in the phoenix, how many birds, and thousands of stone food.
Is there really 100 birds in Su Shi’s paintings, or only 8 birds? The original poet used the method of integer splitting in number theory to divide 100 into two 1, three 4, five 6 and seven 8 sums, including Unexplainedly implement the "hundred" word in the bird map:
1+1+3×4+5×6+7×8=100
It is unique.
The problem of splitting integers, that is, the problem of dividing a positive integer into a number of positive integers according to certain conditions, is a very active mathematical branch in number theory and combination theory, which involves extensive and difficult mathematical theory. "Göderbach's conjecture" can also be seen as the sum of two prime numbers. The splitting of integers is also a common modification in poetry.
It is worth noting that many famous poets in ancient times expressed their unclearness in their works, especially when they have obvious exaggerations, strong feelings and mysterious large numbers. They all like to use some 2,3 , 5, the number multiplied by the prime factor, such as:
The flow is three thousand feet straight down, and it is suspected that the Milky Way falls for nine days.
3000=
There are three hundred lychees, and they will grow up as neighbors.
Fables are an important form of literary works. They have always given profound revelation. The so-called scientific fables in fables, some of its materials are directly derived from mathematical knowledge.
There is such a fable: a prime minister of ancient India, invented a kind of "willing chess" for the king to entertain. The king is very happy for this. He asked the prime minister to make a reward for himself. The prime minister asked for the 64 squares he invented. Put some grain in the board, put 1 grain in the first grid, 2 capsules in the second grid, and 4 capsules in the third grid. According to this, the grain in the next grid is doubled compared with the previous grid. King The next day, the king's finance minister rushed to report, he counted the country's wheat reserves, and could not honor the reward. The sum of the series can be used to calculate the grain required by the prime minister. The number is:
According to estimates, a cubic meter of warehouse can graze wheat, and the number of grains required for primed phase is that it needs cubic meters of storage. If the warehouse is 4 meters high and 10 meters wide, its length needs kilometers, which is equal to The distance between the earth and the sun is twice or 7000 times longer than the Earth's equator. The total number of wheat in the world, the working people of the world will be produced at least 2000 years, what will the king do to cash it, and one, one person When you buy land on the grassland, the seller sells land in a special way. As long as you pay 1000 rubles, he can start from the sun in one day, start at any point on the grassland, walk on the grassland to the sun, before sunset. He returned to the starting point, and the land surrounded by the route he took every day, even if he bought it. Although this person walked back to the place on time, he died immediately because he was physically weak. How did he go first? He walked 10 miles in a straight line, then turned left 90, and continued to move 2 Russians. At this time, he found that the weather was not too early, he had already traveled 24.7 ounces. So he had to Change the direction of progress, run directly to the starting point. Finally at sunset He ran 15 nautical miles before. He ran 42.35 kilometers on this day and surrounded the land of about 86.72 square kilometers! The route he took was a right-angled trapezoid, which is a very unreasonable way of walking. Everyone knows that if you take a square and divide it into the same area, you only need to walk 37 kilometers and walk 5 kilometers less. If you run a circle and enclose the same amount of land, you only need to run 33 kilometers. It is only the distance he runs. 78%, maybe not exhausted! The first model network to organize the article...
In any era, the civilization of any country can be reflected through its architecture. Architecture is not only a symbol of comprehensive technology, but also a symbol of spiritual civilization. Just like the architectural structure of the inner city of Beijing, Zhengyangmen, Tiananmen, Wumen, Taihe Hall The Jingshan, Drum Tower and Bell Tower are located on the north-south axis of the eight-kilometre long distance. The palaces on both sides are symmetrically distributed. The Kowloon throne on the Hall of Supreme Harmony is also placed on this central axis. Wanchun Pavilion on Jingshan is Beijing. The geometric center of the inner city. Here, how much will also express the essence of the supremacy of the imperial power.
The style of architecture, the aesthetic requirements of architecture, is also a reflection of mathematical thinking.
In daily life, a simple regular composition can be a visually filled blank for a flat fill. It has been noted that it is generally used to align a regular pattern of a flat surface. What are the different types of flat surfaces? The key is that each regular pattern is joined. At one point, whether the integer multiple of the inner angle is equivalent to the same apex angle.
We can do the following operations: Let m positive n-edges join at a point on the plane, since each inner angle of the positive n-gon is × 180 /n = 360, thus: × 180 /n =360
m
n
Graphics
3
6
hexagon
4
4
quadrilateral
5
3.5
------
6
3
After simplification of the triangle, mn-2m-2n+4=4
M-2=4
=4→*
According to *, you can choose the relationship between the sum and the polygon of the tile plane as follows:
It can be seen that there are only three options for the regular graphic tiling plane. However, the three basic graphics can evolve other colorful patterns. Therefore, the paving problem has always been a problem of interest to mathematicians and building materials vendors.
Mathematics is not an indifferent fact and data. Russell said: "Mathematics, if you look at it correctly, not only has the truth, but also the supreme beauty, just like a serious beauty in the sculpture. Ever, the mathematics in life for adulthood For people, it is very simple and easy to find. As a student, living in this age of information, we should apply the scientific knowledge we have learned to real life and apply what we have learned!
"Practice tests the truth." This is the famous saying of Deng Xiaoping, the chief architect of the great reform and opening up. The mathematics in life embodies the practicality of the basic discipline of mathematics. It is the origin of life, the mathematics in life. From the market, between the buyers and sellers, to the construction of a skyscraper, the wonders of the world. All the famous works of the masters of art, all use mathematics. Similarly, there is a great connection between mathematics and various disciplines. Physics, chemistry, and even Chinese. In the creation of literature, the use of some mathematical things will make the works more philosophical.
What is mathematical beauty? This sounds like a subjective and arbitrary question. In fact, the mathematical theory itself is peculiar, subtle, concise and powerful. The creative thinking of human beings when establishing these theories is the beauty of mathematics. A correct mathematical theory reflects the objective things. Essence and law, this is the truth of mathematics; no matter how far away from reality, mathematical theory can always find its practical use and reflect its value orientation for human service. This is the goodness of mathematics. When people talk about humanistic spirit Often, the humanistic spirit is positioned at the highest level of pursuing "truth, goodness, beauty" and the comprehensive and free development of human beings. Mathematics is the unity of truth, goodness and beauty.
All along, mathematics gives our students the feeling that it is a headache, a strange symbol, an abstract concept that makes people look annoyed. If the sentence is not read, the symbol is not known, and where is the aesthetic taste. There is a song on the tracing copybook used by primary school students in China:
One two three four five, Jinmu water fire soil.
Heaven and earth are divided, the sun and the moon are the same.
In just 20 words, it contains extremely rich content. One two three four five is the smallest natural number. On the one hand, it is like the "rejuvenation" of poetry, it has a total effect, on the other hand. Refers to all quantitative relationships. Jinmu Shuihuo is the basic element that the ancients believed to constitute the material world, representing the material world. The ancients also used some natural numbers to correspond to it. The third sentence describes the vastness of the universe, and the fourth sentence describes the eternal time. It can be seen that in this short 20-word song, the quantity, the material, the time and the space are all linked together, the colorful and material world, the vast and magical space, the colorful, the beautiful, all unified in quantity. In the middle, look at the following:
a frog with a mouth,
Two eyes, four legs,
Ploped into the water.
For example, a frog corresponds to a mouth, from which there is a mapping knowledge about mathematics, which has one-to-one knowledge; and so on, two frogs have two mouths. Also, the eyes of the frog and Legs, you can apply the algebra knowledge of multiplication. A frog has two eyes, four legs, then, n frogs have 2n eyes, 4n legs.
Su Shi, a writer of the Song Dynasty, not only wrote poems well, but also made calligraphy paintings. At one time, he painted a picture of "Hundred Birds Returning to the Nest", a champion named Lun Wenxu in Guangdong, in his Painting a poem:
Returning one more one, three four five six seven eight.
How many birds in the phoenix, how many birds, and thousands of stone food.
Is there really 100 birds in Su Shi’s paintings, or only 8 birds? The original poet used the method of integer splitting in number theory to divide 100 into two 1, three 4, five 6 and seven 8 sums, including Unexplainedly implement the "hundred" word in the bird map:
1+1+3×4+5×6+7×8=100
It is unique.
The problem of splitting integers, that is, the problem of dividing a positive integer into a number of positive integers according to certain conditions, is a very active mathematical branch in number theory and combination theory, which involves extensive and difficult mathematical theory. "Göderbach's conjecture" can also be seen as the sum of two prime numbers. The splitting of integers is also a common modification in poetry.
It is worth noting that many famous poets in ancient times expressed their unclearness in their works, especially when they have obvious exaggerations, strong feelings and mysterious large numbers. They all like to use some 2,3 , 5, the number multiplied by the prime factor, such as:
The flow is three thousand feet straight down, and it is suspected that the Milky Way falls for nine days.
3000=
There are three hundred lychees, and they will grow up as neighbors.
Fables are an important form of literary works. They have always given profound revelation. The so-called scientific fables in fables, some of its materials are directly derived from mathematical knowledge.
There is such a fable: a prime minister of ancient India, invented a kind of "willing chess" for the king to entertain. The king is very happy for this. He asked the prime minister to make a reward for himself. The prime minister asked for the 64 squares he invented. Put some grain in the board, put 1 grain in the first grid, 2 capsules in the second grid, and 4 capsules in the third grid. According to this, the grain in the next grid is doubled compared with the previous grid. King The next day, the king's finance minister rushed to report, he counted the country's wheat reserves, and could not honor the reward. The sum of the series can be used to calculate the grain required by the prime minister. The number is:
According to estimates, a cubic meter of warehouse can graze wheat, and the number of grains required for primed phase is that it needs cubic meters of storage. If the warehouse is 4 meters high and 10 meters wide, its length needs kilometers, which is equal to The distance between the earth and the sun is twice or 7000 times longer than the Earth's equator. The total number of wheat in the world, the working people of the world will be produced at least 2000 years, what will the king do to cash it, and one, one person When you buy land on the grassland, the seller sells land in a special way. As long as you pay 1000 rubles, he can start from the sun in one day, start at any point on the grassland, walk on the grassland to the sun, before sunset. He returned to the starting point, and the land surrounded by the route he took every day, even if he bought it. Although this person walked back to the place on time, he died immediately because he was physically weak. How did he go first? He walked 10 miles in a straight line, then turned left 90, and continued to move 2 Russians. At this time, he found that the weather was not too early, he had already traveled 24.7 ounces. So he had to Change the direction of progress, run directly to the starting point. Finally at sunset He ran 15 nautical miles before. He ran 42.35 kilometers on this day and surrounded the land of about 86.72 square kilometers! The route he took was a right-angled trapezoid, which is a very unreasonable way of walking. Everyone knows that if you take a square and divide it into the same area, you only need to walk 37 kilometers and walk 5 kilometers less. If you run a circle and enclose the same amount of land, you only need to run 33 kilometers. It is only the distance he runs. 78%, maybe not exhausted! The first model network to organize the article...
In any era, the civilization of any country can be reflected through its architecture. Architecture is not only a symbol of comprehensive technology, but also a symbol of spiritual civilization. Just like the architectural structure of the inner city of Beijing, Zhengyangmen, Tiananmen, Wumen, Taihe Hall The Jingshan, Drum Tower and Bell Tower are located on the north-south axis of the eight-kilometre long distance. The palaces on both sides are symmetrically distributed. The Kowloon throne on the Hall of Supreme Harmony is also placed on this central axis. Wanchun Pavilion on Jingshan is Beijing. The geometric center of the inner city. Here, how much will also express the essence of the supremacy of the imperial power.
The style of architecture, the aesthetic requirements of architecture, is also a reflection of mathematical thinking.
In daily life, a simple regular composition can be a visually filled blank for a flat fill. It has been noted that it is generally used to align a regular pattern of a flat surface. What are the different types of flat surfaces? The key is that each regular pattern is joined. At one point, whether the integer multiple of the inner angle is equivalent to the same apex angle.
We can do the following operations: Let m positive n-edges join at a point on the plane, since each inner angle of the positive n-gon is × 180 /n = 360, thus: × 180 /n =360
m
n
Graphics
3
6
hexagon
4
4
quadrilateral
5
3.5
------
6
3
After simplification of the triangle, mn-2m-2n+4=4
M-2=4
=4→*
According to *, you can choose the relationship between the sum and the polygon of the tile plane as follows:
It can be seen that there are only three options for the regular graphic tiling plane. However, the three basic graphics can evolve other colorful patterns. Therefore, the paving problem has always been a problem of interest to mathematicians and building materials vendors.
Mathematics is not an indifferent fact and data. Russell said: "Mathematics, if you look at it correctly, not only has the truth, but also the supreme beauty, just like a serious beauty in the sculpture. Ever, the mathematics in life for adulthood For people, it is very simple and easy to find. As a student, living in this age of information, we should apply the scientific knowledge we have learned to real life and apply what we have learned!
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