最近仔细阅读了单先生编著的《算两次》.书中谈到,算两次是一种重要的数学方法,也称为富比尼(G.Fubini)原理.减法运算完后用加法运算检验其结果,除法运算完后用乘法运算检验其结果,都属于“算两次”.为了得到一个方程,我们必须把同一个量用两种不同的方法表示出来,这也属于“算两次”.不仅计算题、求解题需要这样做,在证明中,用两种方法计算同一个量,更是一种行之有效的基本方法.该书中举了大量精巧的例子来说明算两次确实是一种应用广泛的数学方法.最后,单先生指出:“算两次,即从两个方面来考察.……某些时候用‘转换观点’,‘换一个角度看问 Recently, I read carefully the “Calculation of Two” edited by Mr. Shan. The book says that counting twice is an important mathematical method, also known as G.Fubini’s principle. After subtraction, it uses addition. To test the result, after dividing the operation and testing its result with multiplication, all belong to “calculate twice.” In order to get an equation, we must express the same quantity in two different ways. This also belongs to “calculation twice. ”. Not only do calculations and solving problems need to be done. In the proof, using two methods to calculate the same quantity is an effective basic method. The book gives a lot of exquisite examples to illustrate the two This time is indeed a widely used mathematical method. In the end, Mr. Shan points out: “Calculate twice, that is, from two aspects... . Sometimes with ’convert views’, ’to look at an angle