-About the Application of Axisymmetric Graphics
The world of mathematics is really vast. From point to line, from line to surface, from surface to body. Have a wealth of knowledge. I remember a famous saying: Mathematics is much bigger than science because it is the language of science. It is conceivable that the greatness and charm of mathematics!
However, in the big family of mathematics. I am deeply attracted by a pair of brothers. Their shape, their relationship and their universality make people feel that they are always around us and very close to us. They are axisymmetric figures.
Axisymmetric graphics are graphics that must be folded along a straight line, and the parts on both sides of the straight line overlap each other. The reason for their relationship is that they are always connected by a straight line, like a pair of inseparable brothers, and their relationship is very close. The straight line that pulls them together is their axis of symmetry. Of course, this axis of symmetry is like a fair judge. The length, area and size of the left and right sides are not bad at all, the only difference is the direction they face.
In the math textbook, we saw their figures, and also contacted and understood them. But what impressed me more was the graphics or things they played and constituted in their daily life.
1. Axisymmetric graphics in life
1, an axisymmetric figure in nature
When I walk in the street, I often see butterflies flying around. When a butterfly stays on a flower and spreads its wings, I find that if the midpoint of the butterfly's two tentacles is connected with its tail, the straight line where the connected line segments are located is its symmetry axis. The right wing is like a figure in which the left wing flips along the symmetry axis. There are many animals with axisymmetric figures like butterflies. Such as dragonflies, moths and so on. If it is autumn, looking at the rice fields from afar, I can't help but feel that it is another harvest season. In this happy season, I walked on the path near the field and picked up a golden leaf. After careful observation, I found that leaves also have symmetry axes. If we regard the meridian in the middle of the leaf as the symmetry axis of its left and right sides, then we will fold the right part of the leaf in half along this symmetry axis, which coincides with the left part of the leaf.
2. Axisymmetric graphics in trademarks
Once, my family and I went to China Bank to withdraw money, and accidentally found that the logo of China Bank was also an axisymmetric figure. There are two symmetry axes in this graph. The first line is formed by connecting two vertical lines in the icon, the other line is the midpoint of the line segment connected by the upper and lower horizontal lines in the box, and the straight line is its second symmetry axis. Such as China Bank, China Unicom, China Agricultural Bank and Mercedes-Benz. However, if you don't think the previous examples are usually noticed, then the examples mentioned below must be familiar to you. This example is a trademark. I will give you one first. My biggest interest is to eat snacks. So I am very familiar with the trademark "Want Want". I found that in the trademark Want Want, the midpoint of a line segment between the heels of two feet is the midpoint of its hair, and the straight line where the line segment to be connected is its axis of symmetry. It is this axis of symmetry that divides the icon Want Want into two equal parts. There are many symmetrical trademarks like Want Want. For example, the trademarks of Wuliangye, McDonald's, Converse and so on. These figures are common in our daily life, which does not tell us that mathematics is everywhere as long as we observe life carefully.
Second, the axisymmetric graphics in architecture
After talking about the common and common axisymmetric figures in life, we should also talk about the grand axisymmetric buildings in the building. Like Tiananmen Gate in China. If a line segment is used to connect the left and right sides of Tiananmen Gate, the straight line where the midpoint of this line segment is located is the axis of symmetry. Doesn't this axis of symmetry divide Tiananmen Gate into two identical parts? The Eiffel Tower in France is one of the landmark buildings in France. Its symmetry axis is the two sides connecting the bottom of the tower. The midpoint of the connected line segment is in a straight line with the spire. There are also some buildings that use axisymmetric methods. They built a large pool in front of the building, which made the building reflected in the water, thus forming an axisymmetric effect, increasing the space and making the original building more beautiful and spectacular. Like the Taj Mahal, it is the best example of the combination of architecture and axisymmetric graphics. On the other side of the earth, there is a building that deeply affects the history of the whole world. This building is the White House. This is the famous administrative building in Washington, USA. Behind the rise of the White House, axial symmetry has played an extremely important role. The symmetry axis of the White House is a straight line connecting the point at the top and the midpoint of the left and right line segments at the bottom. By the way, each of us will have a door at home, and some architects want to make the door look more solemn. The door is designed in this way, the left and right sides of the door are the same, and the doors of ancient yamen and some official residences are also designed in an axisymmetric form. Make the gate look more imposing and dignified. From this, we can easily find that as long as we understand the axisymmetric graphics and are good at using them, we can integrate them into all aspects.
3. Axisymmetric figures in the literature
1, axisymmetric figure in the text
As we all know, our Chinese nation has a long culture of 5000 years. So many years of culture have precipitated countless treasures. Paper-cutting is one of the oldest folk arts in China. Even in this work of art, there are many axisymmetric applications. Let me give you an example. I still remember when my grandmother taught me to cut the traditional Chinese character "Xi", I first folded the red paper in half and then swayed it on the paper with scissors for a while. When I opened the paper that had just been folded in half, the word "hi" appeared. I was happy and surprised after reading it, but I didn't know why. Now that I have grown up, I also know that in fact, in the process of cutting the word "Xi", axial symmetry is also used. There are many paper-cut works, and it is precisely because of the existence of axial symmetry that they are more exquisite and beautiful. Of course, in the simplified characters we are writing now, there is also axial symmetry. Such as "abundance", "eye" and "sharpness". The symmetry axis of characters is easier to find. Basically, you can find it horizontally and vertically. In fact, sometimes, the symmetry axis also has the function of replication. It can divide a word into two identical words, like "two". If its symmetry axis is regarded as the straight line where the line segment connected by the midpoint of the first horizontal line and the midpoint of the second horizontal line is located. Then, can't the patterns on the left and right sides be approximately regarded as two twos? At this time, axis symmetry has the function of replication, but in my eyes, it has another function. Take this "one" for example. As before, it is also the axis of symmetry of vertical painting. After painting, take this symmetry axis as the original words, and you will find it. "One" and this symmetry axis form a "ten". This is the second function of axisymmetric graphics in my eyes. Can change one word into another.
2. Axisymmetric figures in the literature.
What I just said is the application of axial symmetry in this paper. What about sentences made up of words? Actually, if you think about it, there are. I remember playing a game with my classmates in the past, in which one person said a word and the other person immediately read it backwards. During the whole competition, I was deeply impressed by a sentence "Shanghai tap water comes from the sea". When we read this sentence backwards, we will find that it is exactly the same as the word order we are reading. Take a closer look, this is another application of axial symmetry. Let's just say that if we don't look at the word "Shanghai tap water comes from the sea", then the straight line where the midpoint of the word "Lai" is located can divide this sentence into two equal parts. Doesn't this prove that there are also axisymmetric applications in sentences? This series of examples also show us the achievements of axisymmetry in literature, which can make some works more perfect and have the function of making the finishing point. It can also change words and make sentences smooth. It brings more interest to words and sentences and adds a very beautiful stroke to literature.
4. Axisymmetric graphics in the Olympic Games
The 2008 Beijing Olympic Games is coming. In this grand gathering, people all over China are very excited, and people from all over the world participate in different forms. It is not difficult for us to find an axisymmetric figure-the Olympic five-ring flag.
We can connect the Olympic five-ring flag (as shown in figure 1). The point A where the yellow ring contacts the green ring and the point B on the black ring, and the symmetry axis is the straight line where the line segments A and B are located.
In the Olympic Games, there are five Olympic rings and mascots. The mascot of the 2008 Beijing Olympic Games is the Olympic Fuwa. A closer look at our Olympic Fuwa can't help but make people like it. Especially Fuwa Jingjing is charming. His simplicity and simplicity give people a sense of intimacy. Figure 2 is a picture of Fuwa Jingjing lifting weights. If you look at the picture in Figure 2, you will find that if you connect the point A in this picture with the point B at the bottom. Then the straight line where this line segment is located is the symmetry axis of Fuwa Jingjing. Surprisingly, the original Olympic Fuwa is also an axisymmetric figure.
Also at the Olympic Games, when the national flags of various countries slowly rose, it triggered my association with axisymmetric graphics. Like the British flag, its symmetry axis is a straight line connecting the midpoint of the upper and lower line segments of the national flag. There are many national flags like this. For example, the Canadian flag, the Italian flag and so on.
The ever-changing axisymmetric graphics make me dazzled and dizzy. In every change, you can find many surprises. Axisymmetric change is also ubiquitous, it exists in every corner, which also brings us a lot of convenience to study it.
In the process of studying axisymmetric figures, I learned that mathematics can only be discovered by careful observation. Only by understanding mathematics and using it well in life can mathematics be integrated into all aspects. Only by integrating mathematics into all aspects can we learn mathematics better.
In fact, the world of mathematics is really big. At this time, I really want to turn myself into a mountain and stand in the forest of mathematics. Into running water and mathematics, into floating white clouds in mathematics, into flying birds in mathematics.
I sincerely hope that everyone will discover mathematics with the eyes that discover beauty! Feel the math!