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借用一类问题的性质和解法来研究另一类问题的思维方法是解数学题的一个重要原则,构造法便是这个原则的具体体现。 所谓构造法就是根据数学问题的题设或结论所具有的特征、性质或者数量关系,构造出满足条件或结论的数学模型,借助于该模型解决数学问题的方法。这里所说的数学模型是指对数学问题的特征或数量关系,采用形式化的数学语言,概括地表达出来的一种数学结构。例如各种数系、方程、函数、多边形、圆以及多面体等等。因为它们都是从客观事物的某种数量关系或者空间形式抽象得来的数学概念,并且各个概念都有专用的符号,所以这些数学概念都可以看作数学模型。
Borrowing the nature of a problem and the solution to another type of thinking method of thinking is an important principle of solving mathematical problems, construction method is a concrete manifestation of this principle. The so-called construction method is based on the mathematical problems or conclusions of the characteristics, the nature or the number of relations to construct a mathematical model to meet the conditions or conclusions, with the help of the model to solve mathematical problems. The mathematical model referred to here refers to a mathematical structure summarized in terms of the characteristics or quantity of mathematical problems and the formal mathematical language. For example, a variety of numbers, equations, functions, polygons, circles and polyhedra and so on. Because they are all mathematical concepts derived from some quantitative relationship of objective things or spatial abstract, and each concept has a special symbol, these mathematical concepts can all be regarded as mathematical models.