射影几何观点下圆切线作法的理论研究与应用

Theoretical Study and Application of Circular Tangent in Projective Geometry

利用射影几何二阶曲线切线作法探讨欧式几何圆的切线作法,揭示了射影几何与欧式几何圆切线作法的内在联系,解决了圆切线相关的几何问题,使几何证明与作图相统一,对于椭圆、双曲线、抛物线都成立,从宏观角度给出问题的本质属性。

Through using the tangent method of second order curve of projective geometry,the research discusses the tangent method of Euclidean geometric circle,reveals the internal relation between projective geometry and Euclidean geometric circular tangent method,and solves the geometric problems related to circular tangent,so that its geometric proof and drawing are unified.And this also exists in ellipse,hyperbola and parabola.The essential attributes are provided from the macro-perspective.