Reduction is a common mathematical thought and method, which means that a complex problem or mathematical problem is reduced to another or several simpler problems or known mathematical problems by some transformation means, so as to get the answer to the original problem. The basic idea of reduction method is to gradually transform the problem, from complex to simple, from unknown to known.
When solving mathematical problems, we often break down complex problems into several simpler ones, or convert unknown quantities into known quantities, thus simplifying the complex and turning the difficult into the easy.
When solving a complex mathematical equation, we can simplify it into several simple equations, then solve these simple equations respectively, and finally get the solution of the original equation according to the solutions of these simple equations. For example, when solving some geometric problems, we can reduce them to some known geometric theorems or axioms, and then use these theorems or axioms to solve them.
Characteristics of reduction method:
1. Simplify: Simplify a complex problem into several simpler problems, thus making the problem easier to solve. This method can help us to reduce the difficulty of the problem, turn the complex problem into a series of simple problems, and find the solution to the problem more easily.
2. Turn the unknown into the known: the reduction method converts the unknown into the known, so that the unknown can be solved by the known. This method can help us better understand the problem, turn the unknown problem into a known problem, and find the answer to the problem more easily.
3. Turn the part into the whole: The reduction method is to decompose a problem into several simple problems, so that the problem can be solved as a whole. This method can help us better grasp the overall situation of the problem, break a problem into several parts, and thus it is easier to find a solution to the problem.
4. Abstraction into concreteness: reduction turns abstract problems into concrete problems, thus making the solution of problems more intuitive and concrete. This method can help us better understand the problem, turn abstract problems into concrete problems, and find the answer to the problem more easily.