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文献[1]运用三角形相似、圆等有关知识,利用直尺和圆规作出了符合要求的三角形面积平分线,并给出两个推论。笔者研究后发现其中的推论1有待商榷,本文拟对文献[1]中尺规作图的方法进行再思考,并尝试用代数方法寻求尺规作图新方法,从而对过一定点的三角形面积平分线的条数做出判断,限于篇幅,这里仅讨论过三角形形内一点的情形。1原文呈现及反例文献[1]的推论1:在同一平面内,经过三角形重心有且只有三条直线平分这个三角形的面积。经过除重心外的任意一点有且只有一条直线平分这个三
Literature [1] uses the similarity of triangles, circles and other related knowledge, using the ruler and compasses to meet the requirements of the triangle area bisector, and gives two corollaries. The author of the study found that one of the corollary 1 to be discussed, this paper intends to document [1] the rules of the middle of the scale to rethink, and try to use algebraic method to seek a new method of rule mapping, and thus over a certain point of the triangular area Judging from the number of bisectors, due to limited space, only a little bit of the triangle shape is discussed here. 1 Original and Inverse Example [1] Corollary 1: In the same plane, after the center of gravity of the triangle there are only three straight lines bisecting the area of this triangle. After all but the center of gravity and there is only one straight line bisects the three