关于四面体中一个恒等式的研究摘要 在中学教学中,四面体的相关问题常常作为典型题目进行考察,其相关问题也涉及较广,包括等量关系,不等式,体积,面积,最值等.同时四面体中也存在许多的恒等式,各方面学者也对其进行了研究.对于不同类型的恒等式,往往也采取不同的解决方法进行处理、运算,例如通过三角函数法,几何法,代数法等进行解决.本文首先从一个向量恒等式着手,研究向量恒等式的其他解题方法,并对其进行进一步的推广,再利用赋值的方法来研究一些具有代表性的结论.进而在继续研究四面体中的其他恒等式,通过构建向量来进行证明,将向量的各种内容和立体几何相联系.希望得到的结论,和使用方法能够运用到解题过程中,从而提高解题速度,在处理问题上更加快速,简便.关键词 四面体 恒等式 向量恒等式 向量 Study of an identity in a tetrahedronAbstract In middle school teaching, the related problems of tetrahedron are often investigated as typical problems, and their related problems are also involved in a wide range, including equal relation, inequality, volume, area, maximum value and so on. At the same time, there are many identities in tetrahedron, which are also studied by various scholars. For different types of identities, different solutions are often adopted to deal with and operate, such as through trigonometric function method, geometry method, algebraic method and so on. In this paper, we start with a vector identity and study other methods of solving the vector identity. Then we use the assignment method to study some representative conclusions. Then, we continue to study other identities in tetrahedron, and prove by constructing vector, and relate the contents of vector to solid geometry. Hope that the conclusion, and the use of the method can be applied to the process of problem solving, so as to improve the speed of problem solving, in dealing with the problem more quickly easily.Keywords tetrahedron identity vector identity vector...
