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本刊1992年第4期了刊登了题为《浅谈中学物理倒数关系的数学推导模型》的文章,清楚地叙述了类似“1/R=1/R_1+1/R_2”、“1/C=1/C_1+1/C_2”等关系式的推导过程都符合数学中的双曲线模型。那么,推导出来后的这些倒数关系又可归入哪一类的数学模型? 数学中把n个非负实数a_1、a_2……a_n组成的,形式如“n/(1/a_1+1/a_2+……1/a_n)”的式子称为这组实数的调和平均。我们可以把中学物理中的倒数关系略加变形,使之成为调和平均的数学形式。这种变形、归类的目的不仅在于找出一个共同的数学模型,更重要的是可以利
In the 4th issue of the magazine published in the 4th issue of the article entitled “A mathematical derivation model for the physics reciprocal relationship in middle schools”, it clearly describes similar “1/R=1/R_1+1/R_2” and “1/C. The derivation process of the relationship such as =1/C_1+1/C_2“ is consistent with the hyperbolic model in mathematics. Then, what kind of mathematical model can be classified into these inverse relations after derivation? In mathematics, we include n non-negative real numbers a_1, a_2,..., a_n in the form of “n/(1/a_1+1/a_2+ The formula for ...1/a_n)” is called the harmonic mean of this set of real numbers. We can slightly distort the reciprocal relationship in middle school physics to make it the average mathematical form of reconciliation. The purpose of this transformation and classification is not only to find a common mathematical model, but more importantly,