The pedal curve of an epicycloid
(1)
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(2)
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with pedal point at the origin is
(3)
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(4)
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For an -cusped epicycloid with , the pedal curve with pedal point at the origin is
(5)
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(6)
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Noting that
(7)
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(8)
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so solving for gives
(9)
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and plugging in gives a polar equation of
(10)
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which is the equation of a rose curve (Lawrence 1972, p. 204).