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. Starting with familiar problems, the author Academician Zhang Jingzhong vividly introduced how mathematicians found and drew extraordinary conclusions from these simple 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.