Mathematicians have different eyes from ordinary people: problems that are very complicated in the eyes of ordinary people become extremely simple in the eyes of mathematicians; Ordinary people think it is quite simple, and mathematicians may think it is very complicated. The author, Academician Zhang Jingzhong, vividly introduced how mathematicians found and drew extraordinary conclusions from these simple problems, starting with familiar problems. Mathematicians' eyes are not about the skills to solve a certain kind of mathematical problems. It tells us the ideas and methods of thinking about mathematical problems and makes it easier for us to do them.

Mathematicians' eyes can see that "the sum of the internal angles of a triangle is 180" and "the sum of the external angles of any N-polygon is 360", and they can also see that "the sum of the angle changes is 360 when an ant crawls around an ellipse". How can such eyes not be amazing?

Draw a line segment with a compass, and the average person immediately responds: How is it possible? If we think according to the routine, we may answer: "If we use the compass as a pencil and cooperate with a ruler, can't we draw line segments?" However, if you can only draw an absolute straight line with compasses and have no other tools, you may have to think about it. Think about it, what if you don't insist on flying? Use a hollow round jar, put the paper roll into the cylinder, fix the center of the circle in the center of the jar, turn the compass and draw a circle on the paper inside the jar. As soon as the paper is taken out, the line segment is completed!

Chickens and rabbits live in the same cage. What can mathematicians see from the math problems in this primary school? It will be very simple to solve the equation of chicken and rabbit in the same cage, but it can be solved by the most primitive method besides the equation. Some people may laugh: why use such a stupid method when there is a simple method? But on the other hand, if the formula of chicken and rabbit in the same cage is taken as an equation, then the equation is difficult to solve, isn't it easy?

Mathematicians' eyes can see complex theories from basic mathematical knowledge, possibilities from the impossible and solutions from simple problems. In the eyes of mathematicians, the most basic theory can also be extended to profound mathematical problems. The field of mathematics is infinite, and the real key lies in ourselves. If we carefully observe things around us, grasp ordinary facts, think, explore and explore, we will find mathematics intriguing and ubiquitous. Mathematicians can see the shadow of mathematics from washing clothes, so we can certainly see mathematics from other things. Over time, we will gradually understand and like mathematics. In this way, mathematics is no longer a difficult problem that we rack our brains to think about, but a ubiquitous elf in our lives.

Comment on model essay 2 of the mathematician's eyes

The Eyes of Mathematicians is a popular and refined popular science book written by Academician Zhang Jingzhong of China Academy of Sciences for middle school students. When I first got this book, I really couldn't put it down. I read it all at once, but I didn't write my own thoughts after reading it, because I feel that every time I read an article, I can feel the wonder of mathematics, the sharp eyes of mathematicians and the magical connection of knowledge. That feeling can't be described clearly in words for a while. This is almost my favorite book of all books. The mathematics taught by Academician Zhang Jingzhong is always simple and wonderful. Reading his works is like feeling the wonder of nature. It's wonderful! I've seen it once, and I want to watch it again and again ... and then savor it one by one. Even if I want to write a review now, I can only talk about my feelings on one of the knowledge points.

Mathematics is advanced to some extent, but only mathematicians and math lovers are interested in advanced things. Let's talk about mathematics in life-mathematics in washing clothes. Ordinary people think there is nothing wrong with washing clothes. Why not just wash it? Mathematicians don't think so. First of all, there is a shortage of global water resources, so it is necessary to save water. Secondly, I think the life of a mathematician is always exquisite. He will consider how to wash the cleanest clothes with the least amount of water. This leads to mathematical problems. Of course, mathematicians don't like ambiguity. Make the problem clear first and turn the real problem into a pure mathematical problem. This process is actually the process of establishing mathematical model, that is, the process of using mathematical ideas and knowledge to solve practical problems.

First of all, we must quantify the real problems. If clothes are soaped and rubbed, it is almost impossible to wring them out completely. Assuming that there is still 1 kg dirty water on the clothes, rinse with 20 kg clean water. How can we wash them more cleanly? The book gives detailed answers to each scheme. If 20kg water is rinsed once, the residual dirt on the final clothes is 1/2 1. If you rinse it twice, things will be more complicated. For example, if you rinse with 5 kg of water for the first time, the dirt will be reduced to 1/6, and then rinse with 15 kg, the dirt will be reduced to 1/96. If washed twice with 10 kg of water, the dirt will be reduced to the original 1/66. Of course, you can calculate the cleanliness three times, four times and n times respectively. Finally, the relationship between cleanliness, cleaning times and water use scheme is obtained, which makes the analysis more thorough and clear. But is it that the more times you wash it, the cleaner it will be? Not completely correct, because there are many correct standards in real life, and no matter how clothes are rinsed, the amount of dirty things will not be less than the original 2 to the 40th power. In fact, washing it three or four times is very good. If time consumption and clothing wear are considered, it is a new and more complicated mathematical model. Careful analysis will lead to many unexpected conclusions, which will not be introduced here. If you are interested, you must read the original by yourself. The experience is completely different. Academician Zhang Jingzhong will definitely give you a happy feeling of swimming in the ocean of mathematics.

Look, there is a shadow of mathematics everywhere in elegant life. The truth is everywhere. It seems that the exquisite life still needs mathematics to embellish.

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