1, the combination of numbers and shapes: it is one of the most important and basic thinking methods in mathematics and an effective way to solve many mathematical problems. "Less is not intuitive, but more is difficult to be nuanced" is a famous saying of Professor Hua, a famous mathematician in China, which highly summarizes the role of the combination of numbers and shapes.
2. Transforming ideas: In the whole junior high school mathematics, transforming (transforming) ideas have been running through it. Transforming thinking is to transform an unknown (to be solved) problem into a solved or easy-to-solve problem, such as simplifying the complex, changing the difficult to the easy, changing the unknown to the known, and changing the high order to the low order. It is one of the most basic problem-solving ideas and one of the basic thinking methods of mathematics.
3. Classification idea: The classification of rational numbers, algebraic expressions, real numbers, angles, triangles and quadrangles, the positional relationship between points and circles, straight lines and circles, and the positional relationship between circles are all discussed through classification.
brief introduction
Looking at the college entrance examination questions for many years, skillfully using the thinking method of combining numbers and shapes to solve some abstract mathematical problems can get twice the result with half the effort. The key point of the combination of number and shape is to study "helping number with shape"
The thinking method of combining numbers and shapes is widely used. For example, in solving equations and inequalities, in finding the range and maximum value of functions, in finding complex numbers and trigonometric functions, we can not only find the solution intuitively, but also avoid complicated calculation and reasoning, which greatly simplifies the problem-solving process. This is more advantageous in solving multiple-choice questions and fill-in-the-blank questions. We should pay attention to cultivating this kind of ideology and try to have a picture in our mind to broaden our thinking horizons.