幾何學 : 二邊形

2006-10-24 3:54 am
證明不存在面積大於零的二邊形(兩邊皆直線).
或者
證明任何二邊形的兩條直邊必定完全重疊.

* 最好不要用 極限原理 或 Heron’s formula 證明.

回答 (2)

2006-10-25 11:51 am
✔ 最佳答案
I think it is just a concept problem
A polygon (IPA: [ˈpɒliɡən], from Greek, literally "many-angle") is a closed planar path composed of a finite number of sequential line segments. The straight line segments that make up the polygon are called its sides or edges and the points where the sides meet are the polygon's vertices.
Since a digon (二邊形) has only two lines, it can not composed a closed planar path except that the two sides coincide. In this case, we call it is a degenerate polygon
In mathematics, Area is a quantity expressing the size of a figure in the Euclidean plane or on a 2-dimensional surface. Points and lines have zero area, although there are space-filling curves. Depending on the particular definition taken, a figure may have infinite area, for example the entire Euclidean plane.
Also, the area of a polygon is the measurment of the 2-dimensional region enclosed by the polygon.
Since the 2-dimensional region enclosed by the digon is just a line and the area of the line is 0 (by definition). So, the area of a digon is 0
參考: Wikipedia
2006-10-25 3:28 am
you can use simply equation set (x1,y1) and (x2, y2), as the two side polygon need to start from and end with x1y1, x2y2 then the above two must satisfy.


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