平面曲线对称性的判定

Determine of plane curve's symmetry

平面曲线的对称性对于函数研究具有重要意义。本文给出了平面曲线轴对称与点对称的定义和判定定理,指出可以用类似求一元函数极值和拐点的办法判定曲线的对称轴和对称中心,从而平面曲线的对称性可以归结为导数应用问题。

Symmetry of plane curve is important to function research. This article includes the definition and theorem of exial symmetry and center symmetry, and also points out that the determine of symmetry axis and center of symmetry is similar to calculating extremum and inflexion point of function. So determine of plane curve's symmetry comes down to the application of derivative.