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统编教材《解析几何(平面)》169页规定:“对于平面内任意一点M,用ρ表示线段OM的长度”,而下面又讲:“在某些必要的情况下,也允许取负值”,这显然是矛盾的:既然表示长度,长度是决不允许取负值的,如能取负值,则决不能用它表示长度。长度允许取负值,是令人难以理解的。我认为,如果把“用ρ表示线段OM的长度”,改为“用ρ表示有向线段(?)的数量”既避免了上面所说的矛盾。学生在学习上也容易接受,在应用上也是合理的。理由如下: 1.从角的定义来讲,射线OM是极轴ox绕O点旋转的终止位置,而ox有方向,因此,射线OM是有方向的(实际上,因为OM为射线,就已经知其以O
The textbook “Parsing Geometry (Plane)” on page 169 states: “For any point M in the plane, use ρ to denote the length of the line segment OM”, and the following remarks: “In some necessary cases, negative values are also allowed. ” This is obviously contradictory: Since the length is expressed, the length is never allowed to take a negative value. If it can take a negative value, it can never be used to express the length. The length allowed to take a negative value is incomprehensible. I think that if we change the phrase “use ρ to represent the length of line segment OM” to “use ρ to indicate the number of directed line segments (?)”, we will avoid the contradiction mentioned above. Students are also easy to accept in learning and reasonable in application. The reasons are as follows: 1. From the definition of the angle, the ray OM is the end position of the polar axis ox rotating around the O point, and the ox has the direction, therefore, the ray OM is directional (in fact, because the OM is a ray, it is already Know it with O