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我们知道,完成数学运算所需要的最基本的能力就是数学变形的能力。例如:计算(a+b)~2-(a-b)~2,先把(a+b)~2、(a-b)~2按照完全平方公式展开,然后相减,通过合并同类项,最后变形为一项4ab,这就是所要求得的结果。象这样,在数学变形中,按照给定的法则把几个数或式结合成一个新的数或式我们称之为数或式的“结合变形”。历来,学生在中学数学学习的数学变形主要是结合变形,无可否认,结合变形是最基本的、最重要的数学变形。但是,在另一类数学运算过程中,例如:化简(1+sin2θ)~(1/2)。简单地应用“结合变形“就不够了,我们需要另一种数学变形。众所熟知sin~2θ+cos~2θ=1 2cosθsinθ=sin2θ,这是二
We know that the most basic ability needed to complete mathematical operations is the ability to mathematically deform. For example: Calculate (a+b)~2-(ab)~2, first expand (a+b)~2,(ab)~2 according to the complete square formula, then subtract, merge the same kind of items, and finally transform to A 4ab, this is the result of the request. In this way, in the mathematical variants, according to the given law, several numbers or formulas are combined into a new number or formula, which we call the number or formula. Historically, the mathematics of students’ mathematics in middle school mathematics has been mainly combined with deformation. It is undeniable that combining deformation is the most basic and most important mathematical distortion. However, in another type of mathematical operation, for example: Simplify (1+sin2θ)~(1/2). Simply applying “combination deformation” is not enough, we need another mathematical transformation. It is well known that sin~2θ+cos~2θ=1 2cosθsinθ=sin2θ, which is two