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一、引言本文是前两篇文章“綫段的长度”、“多边形的面积”(分别发表于本刊今年九月和十月号)的續篇。多面体是以簡单多边形为面的封閉空間图形,和面积的概念相似,多面体的体积定义是:多面体A的正实值函数V(A),它滿足下面两条件:ⅰ)两合同的多面体的体积相等,即A≡B时,V(A)=V(B);ⅱ)如果把多面体A剖分成两个多面体B和C,則V(A)=V(B)++V(C)。完全和多边形面积理論相似,从这个定义出发,我們能够証明多面体的体积是存在的,如果我們进一步把边为单位长的立方体的体积定义为1的話,則任意多面体的体积还是唯一的。然后,沿着中学立体几何教科书中的途径,我們能証明許多常見的多面体的体积公式。
I. INTRODUCTION This article is a continuation of the first two articles, “Length of Line Segments,” and “Area of Polygons,” published in the September and October of this issue respectively. The polyhedron is a closed space graph with simple polygons as faces. The concept of area is similar. The polyhedron’s volume is defined as the positive real-valued function V(A) of the polyhedron A, which satisfies the following two conditions: i) The polyhedral of two contracts When the volume is equal, ie, A≡B, V(A)=V(B); ii) If polyhedron A is split into two polyhedrons B and C, then V(A)=V(B)++V(C) . Fully similar to the polygonal area theory, starting from this definition, we can prove that the polyhedral volume exists. If we further define the volume of the cube whose edge is unit length as 1, then the volume of any polyhedron is still unique. Then, along the path in the middle school geometry textbooks, we can prove many common polyhedral volumetric formulas.