# What happens to a rose curve if n=r/s is an irrational number?

Dec 23, 2015

There are an infinite number of petals.

#### Explanation:

If $n$ is odd, the rose curve has $n$ petals.
If $n$ is even, the rose curve has $2 n$ petals.

For rational $n$-values, the curve closes at an angle of $\theta = \pi s p$.
If $r s$ is odd, $p = 1$.
If $r s$ is even, $p = 2$.

For irrational $n$-values, there are an infinite number of petals.

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