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 We next ask: what is the pedal curve of the nephroid relative to its centre? At each point of the nephroid locus we draw the tangent to the curve. For each such tangent we draw a normal throught the centre O, and plot the locus of tangent-normal intersections.
Click the diagram below to activate the applet, and then click the ‘Animate’ button to generate the pedal curve. Clicking the little red x at bottom right will clear the drawing from the applet window. Now drag the red point Q slowly along the segment. Can you describe the construction? Have we seen this curve before?
The resulting pedal curve produced here has a very pleasing shape. It is not dissimilar to the pedal curve of the lemniscate relative to the centre.
Bibliography
A reference to this construction and a brief description of the pedal curve can be found in:
A book of curves, Lockwood E. H., Cambridge University Press, 1967 : Q9 page 69.
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