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r = a + b cos(θ), a/b < 1
Limacon, inner loop
r = a + b cos(θ), a/b = 1
Limacon, Cardioid
r = a + b cos(θ), 1 < a/b < 2
Limacon, dimpled
r = a + b cos(θ), a/b > 2
Limacon, convex
r = a cos n θ
rose curve, n even then double, n odd then keep. a is petal length
r = a cos θ
circle
r² = a² sin 2 θ
lemniscate
r = a² sin 2 θ
lemniscate