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文[1]利用旋转相似变换给出了过平面内任意一点作三角形面积平分线的尺规作图方法,但文后推论“经过除重心外任意一点有且只有一条直线平分这个三角形的面积”是错误的.笔者在GeoGebra环境下,从分析三角形面积平分线的几何特征入手,探索出三角形面积平分线的包络曲线是双曲线,并利用圆锥曲线的几何性质划分出面积平分线的条数存在区域,给出了三角形面积定点平分线和定向平分线的尺规作图新方法.
In [1], a method of ruler mapping is given by using rotational similarity transformation to make any point in the plane be the triangle bisecting area. However, it is deduced that “the area of this triangle is divided by any point except gravity center with only one straight line ”In the context of GeoGebra, starting from the analysis of the geometric characteristics of the bisector of the triangle area, the author finds out that the envelope curve of the bisector of the area of the triangle is a hyperbolic curve, and uses the geometric properties of the conic curve to divide the bisector of the area The number of the existence of the number of regions, given the triangle area fixed point bisector and bisector of the rule rule drawing a new method.