Rose curve

Parametric equations

The rose curve has the form:

When k is an integer, an odd k gives k petals and an even k gives 2k petals.

Interaction

• Petal count k: drag the slider to an integer k. An odd k gives k petals and an even k gives 2k petals. Changing k grows the curve out from the center again

What to notice

• $r=a\cos (k\theta )$ draws symmetric petals in polar coordinates.
• The amplitude $a$ only changes the scale. The number of petals and the symmetry are set by k.
• Where the petals meet, $\cos (k\theta )=0$.

Related

• Lissajous curve
• Spirograph curve
• Harmonograph

Further reading

• Rose (mathematics) (Wikipedia)