使用Mathematica绘制蔓叶线图形(Cissoid of Diocles)

定义:

百度百科:“蔓叶线,有时又叫双蔓叶线是Diocle是在公元前180年发现的曲线。在几何形状中,蔓叶线是从两个给定曲线C1,C2和点O(极点)产生的曲线。”

Wikipedia:“In geometry, the cissoid of Diocles is a cubic plane curve notable for the property that it can be used to construct two mean proportionals to a given ratio. In particular, it can be used to double a cube. It can be defined as the cissoid of a circle and a line tangent to it with respect to the point on the circle opposite to the point of tangency. In fact, the family of cissoids is named for this example and some authors refer to it simply as the cissoid. It has a single cusp at the pole, and is symmetric about the diameter of the circle which is the line of tangency of the cusp. The line is an asymptote. It is a member of the conchoid of de Sluze family of curves and in form it resembles a tractrix.

Mathematica中蔓叶线的绘制:

使用Mathematica绘制蔓叶线图形(Cissoid of Diocles)

扩展知识:蔓叶线的构建及极坐标方程、直角坐标方程的推导过程(清晰易懂)
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以下内容转自 Wikipedia

Construction and equations

使用Mathematica绘制蔓叶线图形(Cissoid of Diocles)

使用Mathematica绘制蔓叶线图形(Cissoid of Diocles)

使用Mathematica绘制蔓叶线图形(Cissoid of Diocles)