摘要：变换的思想是一类重要的数学思想，应用变换的方法去解题可使问题得到简化, 从而在解题中取得很好的效果。数学中的变换有很多种，本文对几种常见的数学变换——正交变换、仿射变换、射影变换总结，将高等几何与初等几何相结合，利用高等几何的相关知识去解决初等几何中的一些证明。在解决的过程中运用两个重要的思想，即转化思想和不变量思想。

关键词：正交变换；仿射变换；射影变换

Abstract：Transformation of thought is a kind of important mathematics thought, applying the transformation methods to solve the problems, the problem is simplified, thereby the problem have achieved very good results. In mathematics, transform has many kinds, several kinds of common mathematical transformation -- orthogonal transformation, affine transformation, affine transformation are summarized, the combination of higher geometry and elementary geometry, use of higher geometry knowledge to solve the elementary geometry proof. In the process of resolving the use of two important thought, that thought and ideological transformation invariants.

Key word：Orthogonal transformation; affine transformation; projective transformation