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众所周知的余弦定理是指下面的数学命题: 设△ABC的三边的长分别为a、b、c,三个内角依次为A、B、C,则 当△ABC为直角三角形时,由余弦定理可得出勾股定理。 可是,在三维欧氏空间,对于四面体是否亦有类似定理呢?答案是肯定的。 事实上,我们有如下令人兴奋的结果:
The well-known cosine theorem refers to the following mathematical propositions: Let the lengths of the three sides of △ABC be a, b, and c, and the three interior angles be A, B, and C, respectively. When △ABC is a right-angled triangle, the cosine theorem is used. Pythagorean theorem can be drawn. However, in three-dimensional Euclidean space, is there a similar theorem for the tetrahedron? The answer is yes. In fact, we have the following exciting results: