Can anyone give me a feeling after reading an essay on mathematician junior high school oh urgent

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Hello. The Mathematician's Vision.

The vision of mathematicians is different from that of ordinary people: problems that are very complex in the eyes of ordinary people become extremely simple in the eyes of mathematicians; What the average person thinks is a fairly simple problem, mathematicians may think is very complex. The author, Academician Zhang Jingzhong, started from the problems we are familiar with, and vividly introduced how mathematicians found and drew extraordinary conclusions from these simple problems.

The Mathematician's Perspective is not about the skills of solving a certain type of mathematical problems, it tells us the ideas and methods of thinking about mathematical problems, and the "shortcuts" that make it easier for us to do problems.

The vision of mathematicians can see from the well-known mathematical common sense that "the sum of the inner angles of a triangle is 180°", "the sum of the outer angles of any n-sided shape is 360°", and "the sum of the changes in the angle of an ant crawling around the oval line is 360°", how can such a vision not make people amazed!

Drawing a line with a compass The average person immediately reacts: how is it possible? If we think by convention, we might:

Use the compass as a pencil, and then use it with a ruler, can't you draw line segments? "But in the case where you can only use a compass and no other tools to draw an absolute straight line, you may need to think about it. Think about it, what if you don't stick to a flat surface?

Use a hollow round jar, roll the paper into a cylindrical shape and put it in, fix the center of the circle on the jar**, turn the compass, draw a circle on the paper on the inside of the jar, and when the paper is taken out, the line segment is completed!

Chickens and rabbits are in the same cage, what can a mathematician's vision see from this elementary school math problem? The solution of the equation with the same cage of chickens and rabbits will be very simple, but in addition to the equation, it can also be solved in the most primitive way. Someone might laugh :

With an easy way, why do you use such a stupid method? But if you think about it backwards and use the square of the chicken and rabbit in the same cage to make the equation, then it is difficult to solve the equation, isn't it?

A mathematician's vision can see complex theories from basic mathematical knowledge, the possibility from the impossible, and the solution to the problem from simple problems. In the eyes of mathematicians, the most basic theories can also be derived and transformed into advanced mathematical problems. The field of mathematics is infinitely vast, the real key lies in ourselves, if we observe the things around us attentively, grasp the ordinary facts, think, explore, and explore, we will find that mathematics is intriguing and ubiquitous.

Mathematicians can see the shadow of mathematics in the laundry, then we must also be able to see mathematics in other things, and over time, we will gradually understand mathematics and like mathematics. In this way, mathematics is no longer a difficult problem for us to rack our brains to think, but a little elf everywhere in life.

If you have any questions, please ask them if they are helpful to you.

I once heard an Olympiad math teacher say that learning mathematics is like a fish and a net; Being able to solve a problem is like catching a fish, and mastering a method of solving a problem is like having a net; So, the difference between "learning math" and "learning math well" is whether you have a fish or a net.

Mathematics is a very thoughtful course, and it is very logical, so it will always give people an illusion.

Geometry in mathematics is interesting, and each figure is interdependent, but also has its own merits. For example, circles. The formula for calculating the area of a circle is s= r2, and we often make some mistakes because the radius is different.

For example, "a pizza with a radius of 9 cm and a radius of 6 cm is equal to a pizza with a radius of 15 cm", in terms of proposition, this question first confuses everyone and gives people an illusion, and cleverly uses the area formula of the circle to make people produce a wrong balance.

Actually, a pizza with a radius of 9 cm and a radius of 6 cm is not equal to a pizza with a radius of 15 cm, because the area of a pizza with a radius of 9 cm and a radius of 6 cm is s= r2 = 92 + 62 = 117, and the area of a pizza with a radius of 15 cm is s = r2 = 152 = 225, so a pizza with a radius of 9 cm and a pizza with a radius of 6 cm is not equal to a pizza with a radius of 15 cm.

Math for Life. Mathematics, like a peak, straight into the sky, just started to climb, it feels very easy, but the higher we climb, the steeper the mountain becomes, which makes people feel frightened, at this time, only people who really love mathematics will have the courage to continue climbing, so people who stand on the peak of mathematics love mathematics from the bottom of their hearts.

Remember, the person standing at the foot of the peak cannot see the peak.