Number of Petals of Even Index Rhodonea Curve

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

  • 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 11$: Special Plane Curves: Four-Leaved Rose: $11.17$
  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): rose
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): rose
  • 2009: Murray R. Spiegel, Seymour Lipschutz and John Liu: Mathematical Handbook of Formulas and Tables (3rd ed.) ... (previous) ... (next): $\S 9$: Special Plane Curves: Four-Leaved Rose: $9.17.$
  • 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): rose
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