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LIMAÇON : Pedal curves
Click the diagram below to open the applet, and then click the ‘Animate’ button to generate the pedal curve of the limaçon with respect to the base point M. Clicking the little red x at bottom right will clear the drawing from the applet window. Now drag the red point Q slowly around the circle. Can you describe the construction? Moving the point K along the horizontal line will change the shape of the limaçon, and hence the pedal curve. You can also choose different positions along the x-axis for the point M. Use the little red x to clear the screen after each such move. Are any of the reulting pedal curves familiar?
Despite all the variability of choice, there is a disappointing lack of recognizable pedal curves here. Nevertheless, we might see this construction as a good way of generating ‘new’ curves which may have interesting properties of their own.
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Because there is a whole family of limaçons, as well as a whole family of ‘pedal points’, the problem of finding the pedal curves becomes much more interesting, if not rewarding!
