# Polar equation for a k-leaf rose: is it possible to define an inner radius?

Is it possible to define a polar equation for a k-leaf rose with an inner radius for a k-leaf rose (as in this image)? I'm familiar with the general equation for a k-leaf rose $$r = \cos(k*\theta)$$ and the corresponding Cartesian equations $$x = \cos(k*\theta) * \cos(\theta)$$ and $$y = \cos(k*\theta) * \sin(\theta)$$ However, I've been unable to use these to come up with an equation that produces a rose with a hollow center. I'm very curious to know if it's possible. Thanks in advance, any insights will be greatly appreciated!

• try $r=\cos(k\theta)+c$ where $c>1$ Jan 5 '16 at 11:32 If you increase the denominator it looks like this You can play with the parameters a bit
• @IanSpeers: I had fun with it. Just adding a larger constant makes the ratio of outer/inner too small to my eye. If you make the additive constant greater than $1$ you can remove the square from the cosine See how you like it. This goes fully to David Quinn's suggestion Jan 5 '16 at 18:55