体积勾股定理的证明

The Proof of Volume Pythagorean Theorem

摘要:

用Cayley-Menger行列式证明：当四面体满足“对棱相等、或对棱的平方和相等”时，存在体积勾股定理：“该四面体的体积的平方等于所围的四个面外凸的直角四面体体积的平方和”，其公式为：V²_ABCD=V²_ABC4+V²_ABD3+V²_ACD2+V²_BCD1(标注见：图1)。

Abstract: The Cayley-Menger determinant  is used to prove that when the tetrahedron satisfies “The same of opposite sides respective, or The same of the sum of squares of opposite sides”, there exists The Volume Pythagorean Theorem: “the square of the volume of the tetrahedron is equal to the sum of squares of the volumes of the four Right Angle Tetrahedrons by Surrounded by external”. The formula is:V²_ABCD=V²_ABC4+V²_ABD3+V²_ACD2+V²_BCD1 (the label is shown in Figure 1).