May someone tell me the equation of a conchord?

A curve studied by the Greek mathematician Nicomedes in about 200 BC , also called the conchloid. It is the locus of points a fixed distance away from a line as measured along a line from the focus point. Nicomedes recognized the three distinct forms seen in this family. This curve was a favorite with 17th century mathematicians and could be used to solve the problems of cube duplication, angle trisection, heptagon construction, and other Neusis constrcutions (Johnson 1975).





蚌線可以斜向方式解決三等分角問題 (古代三大作圖難題之一)

尼科梅德斯發現，蚌線可以斜向方式解決三等分角問題，首先，蚌線的定義如下：

圖片參考：http://steiner.math.nthu.edu.tw/ne01/tjy/euclidean/specialcurve/conchoid(defn).gif


設MN為一直線，O為線外一點。過MN上任一線點P，截取PQ等於給定的固定長度k，則Q的軌跡即是蚌線。






Cartesian equation:

圖片參考：http://steiner.math.nthu.edu.tw/ne01/tjy/euclidean/specialcurve/c2img1500.gif


Polar equation:

圖片參考：http://steiner.math.nthu.edu.tw/ne01/tjy/euclidean/specialcurve/c2img1499.gif








請參考網:
http://steiner.math.nthu.edu.tw/ne01/tjy/euclidean/specialcurve/conchoid.htm






希望可以幫到你.

請參考網:
http://steiner.math. nthu.edu.tw/ne01/tjy /euclidean/specialcu rve/conchoid.htm




希望可以幫到你.