In mathematics, a rose is a sinusoid plotted in polar coordinates. Up to similarity,

<math>\!\,r=cos(k\theta)<math>

One obtains a rose-like graph with <math>2k<math> petals if <math>k<math> is even and <math>k<math> petals if <math>k<math> is odd. Using sine instead of cosine, and vice versa, the graphs differ by a rotation of <math>\frac{\pi}{2}<math> radians—or that <math>\sin(kt + \frac{\pi}{2}) = \cos(kt)<math>, and the graphs coincide.

More interesting results arise when <math>k<math> is a rational. If <math>k<math> is irrational, without bounds on <math>\,\!\theta<math>, a disc results.

External links

• Mathworld article on rose curves (http://mathworld.wolfram.com/Rose.html)