Rose (mathematics)

In mathematics, a rose is a specific plot of the sine (or equivalently cosine) trigonometric function in polar coordinates. If one looks at the plot of sine or cosine with integral phase a, one obtains a rose-like graph with 2a petals if a is even and a petals if a is odd. Using sine instead of cosine, and vice versa, the graphs differ by a rotation of π/2 radians - or that sin at+π/2 = cos at, and the graphs coincide. More interesting results arise when considering when a is a rational or even irrational number. Category:Curves