论文部分内容阅读
通过学习平行四边形的性质与判定,我们了解到过平行四边形的对称中心的任意一条直线都可以把平行四边形分成面积相等的两部分。由此引起对“过多边形内部一点的直线把多边形分成两部分图形面积大小”的研究。通过探究得到:过n边形内部的一点P作各边的平行线,这些平行线与各边(或各边的延长线)围成n个平行四边形,它们的面积分别记作:S1S2S3……Sn,若S1≤S2≤S3……≤Sn,则至少存在一条过点P的直线把这个n边形分成两个部分,使得其中小块图形的面积最小,且最小值是2S1。
By learning the nature and judgment of the parallelogram, we learned that any straight line passing through the center of symmetry of the parallelogram can divide the parallelogram into two parts of equal area. This led to the study of “dividing the polygons into two parts of the graphic area” by a little bit more than a straight line inside the polygons. Through inquisition, we can get that: A point P inside the n-polygon is a parallel line on each side, and the parallel lines and each side (or the extension line of each side) form n parallelograms, and their areas are respectively denoted by S1S2S3. Sn, if S1≤S2≤S3 ... ≤Sn, at least one straight line passing through point P divides the n-polygon into two parts so that the area of the small block pattern therein is smallest and the minimum value is 2S1.