設Γ為一平面曲線而 P 為一定點 , 自P 向Γ所有的切線作對稱點，則所有對稱點所成的圖形Γ1 稱為曲線Γ對定點P 的double pedal curve ,
Γ1 對定點P 的double pedal curve Γ2 稱為曲線Γ對定點P 的2-th double pedal curve , Γ2 對定點P 的double
pedal curve Γ3 稱為曲線 Γ對定點P 的3-th double pedal curve ,…… 。以下是本文主要的結果：結論A：當Γ為一圓形而P
為圓上一點時 , 計算其n−th double pedal curve 的方程式。結論B：當Γ為任意平滑的參數曲線而P 為任意一點時 , Γ的 double pedal
curve 的切線性質。結論C：當Γ為任意平滑的參數曲線而P 為(0,0)時, 計算其n−th double pedal curve 的方程式。
Given a plane curve Γand a fixed point P ,the locus of the reflection of P about
the tangent to the curveΓis called the double pedal curve of Γwith respect to P.We
denote Γ1 as the double pedal curve of Γwith respect to P, Γ2 as the double pedal
curve of Γ1 with respect to P , Γ3 as the double pedal curve of Γ2 with respect
to P ,and so on , we call Γn the n-th double pedal curve of Γwith respect to P.
If Γ is a circle, and P is a point on the circle, we got the parametric equation
of the n−th double pedal curve of Γ with respect to P. And, for any parametric plane
curve Γ; we got the method to draw the tangent of the double pedal curve of Γ.