一类四次李氏卵圆

A Kind of Quartic Li’s Oval

本文给出了李氏卵圆的定义,并给出了卵圆的卵心,卵圆的长半径、短半径和对称半径等相关概念的定义,给出一类四次方程,并证明其为李氏卵圆方程。给出了某些四次方程为李氏卵圆方程的判定定理,给出了此类李氏卵圆的切线方程和法线方程,旋转卵球体的体积公式。最后给出实例与仿真验证,能达到吻合的效果。

In this paper, a definition of Li's oval is provided, and the definitions of the oval center, the long radius, the short radius, and the symmetrical radius of the oval are provided. A kind of quartic equation is given and proved to be an oval equation. This proves some decision theorems for some quartic equations to become the Li's oval equation, the tangent equation and normal equation of the oval and the volume formula of rotating oval ball is provided. Finally, an example is given to verify the effectiveness of the simulation.