Reduction is a very important mathematical thought, which is usually used to solve some complicated problems. When solving mathematical problems, the role of reduction method is mainly reflected in the following aspects:

Simplify a complex problem:

The basic idea of reduction method is to transform a complex problem into one or more simple problems. By breaking down problems into smaller parts, we can understand and solve them more easily.

For example, when solving the area problem of a polyhedron, we can decompose the polyhedron into multiple triangles, then calculate the area of each triangle separately, and finally add up these areas to get the total area of the polyhedron.

Establish the connection between old and new knowledge;

Transformation can also help us to establish the connection between old and new knowledge. When we face a new problem, we can compare it with the problem we have solved and look for similarities and differences. In this way, we can turn a new problem into a problem that we have solved, so as to get a solution to the problem.

Help us understand the nature of the problem:

Reduction can help us better understand the nature of the problem. When we face a complicated problem, we may feel confused and helpless. However, it is easier to understand the essence and key points of the problem when we decompose it into smaller parts by reduction method. This can help us find a breakthrough to solve the problem.

Improve the efficiency of problem solving:

Using the reduction method, a complex problem can be transformed into several simple problems, which can not only improve our problem-solving efficiency, but also reduce our error rate. Because when we solve a complex problem, we may make mistakes because of negligence. However, when we use the reduction method to decompose the problem into smaller parts, we can avoid these mistakes more easily.

In a word, reduction is a very useful mathematical thought, which can help us to establish the connection between old and new knowledge when solving complex problems, improve the efficiency and accuracy of our problem solving, and cultivate our mathematical thinking ability and problem solving ability.