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变换是数学中常见且十分重要的方法,几何变换已形成了完整、系统的理论体系,许多几何问题可利用各种变换作出漂亮的解答。本文给出关于三角形的一类几何不等式的几个变换原则,并举例说明其应用。一、变换原则及其应用为简起见,我们将本文介绍的三个变换原则一同综述于下的定理中定理设P为△ABC平面(非边界)上任一点,从P引BC、CA、AB的垂线,垂足分别是D、E、F,记PA=x,PB=y,PC=z;PD=u,PE=v,PF=w,△ABC的BC、CA,AB边与外接圆半径
Transformation is a common and very important method in mathematics. Geometric transformation has formed a complete and systematic theoretical system. Many geometric problems can make use of various transformations to make a beautiful solution. In this paper, several transformation principles for a class of geometric inequalities of triangles are given, and their applications are illustrated. First, the principle of transformation and its application For simplicity, we will review the three transformation principles introduced in this article together with the following theorems. Theorem Let P be any point on the △ABC plane (non-boundary), referencing BC, CA, and AB from P. The vertical and horizontal feet are D, E, F, respectively, and PA=x, PB=y, PC=z; PD=u, PE=v, PF=w, BC, CA, AB edge and circumcircle of ABC. radius