论文部分内容阅读
学习数学通报1963年第六期发表的文章:“关于解析几何教学的几点注意”,仅就文中论述的几个问题提出商讨意见。 1.该文第二段:“解析几何教学中一些问题的商榷”的例2中有下面的一段论述: “直线的方程是一次的”这种说法是不确切的,应当说“直线的方程可以是一次的”。“可以”这两个字,在此是不能省略的。该文作者提出的论据是:在实数范围内,方程x-y=0和x~3-y~3=0同解,因之,方程x~3-y~3=0也可以说是第一、第三象限的分角线l的方程。实际上方程x~3-y~3=0可以变形为(x-y)(x~2++xy+y~2)=0,从而方程x~3-y~3=0的解包含于方程x-y=0和x~2+xy+y~2=0之中。方程x~3-y~3=
An article published in the sixth issue of the study of mathematics in 1963: “A few notes on analytical geometry teaching”, only the discussion of several issues discussed in the text proposed. 1. In the second paragraph of the article: “Analysis of Some Problems in Geometry Teaching.” Example 2 has the following paragraph: “The equation of a line is once.” This statement is inaccurate. It should be said that “the equation of the line It can be once.” The word “can” can not be omitted here. The author’s argument is: In the range of real numbers, the equations xy=0 and x~3-y~3=0 have the same solution. Therefore, the equation x~3-y~3=0 can also be said to be the first one. The equation of the angle l in the third quadrant. In fact, the equation x~3-y~3=0 can be transformed into (xy)(x~2++xy+y~2)=0, so that the solution of the equation x~3-y~3=0 is included in the equation xy =0 and x~2+xy+y~2=0. Equation x~3-y~3=