Polar equation: r
= a cos(p
)
Click below to see one of the Associated curves.
Definitions of the Associated curves Evolute Involute 1 Involute 2 Inverse curve wrt origin Inverse wrt another circle Pedal curve wrt origin Pedal wrt another point Negative pedal curve wrt origin Negative pedal wrt another point Caustic wrt horizontal rays Caustic curve wrt another point
If p = -1 we have a line.
If p = 1 we have a circle.
If p = 1/2 we have a cardioid.
If p = -1/2 we have a parabola.
If p = -2 we have a hyperbola.
If p = 2 we have a lemniscate of Bernoulli (Jacob Bernoulli).
Sinusoidal spirals were first studied by Maclaurin.
They are not, of course, true spirals.
The pedal curve of sinusoidal spirals, when the pedal point is the pole, is another sinusoidal spiral.
The sinusoidal spiral r = a cos(p) inverts to r = a/cos(p) if the centre of inversion is taken at the pole.
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