Number of Petals of Even Index Rhodonea Curve

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Theorem

Let $n$ be an even (strictly) positive integer.

Let $R$ be a rhodonea curve defined by one of the polar equations:

\(\ds r\) \(=\) \(\ds a \cos n \theta\)
\(\ds r\) \(=\) \(\ds a \sin n \theta\)


Then $R$ has $2 n$ petals.


Proof


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Sources

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