Question

What is a rose curve?

Answer 1

A rose curve or rhodonea curve is a graph of the following polar equation:

r=Acos(kθ)

where k=mn. The polar equation can also be written as two Cartesian parametric equations:

xy=Acos(kt)cos(t)=Acos(kt)sin(t)(1)(2)

The shape of the graph is strongly dependent on the value of k, and the values of m and n can give clues as to what the shape will be. For example, if k is an integer, the graph will look like a classic flower and have 2k petals if k is even, and k petals if k is odd.

If k is half an integer, such as 1.5, 2.5 and so on, the graph will 4k petals but they will overlap which does not occur for integer k. If m=n then we will get a perfect circle.

The user interface above allows you to adjust the values of m and n so you can see how they affect the graph and see if you can figure out the patterns.

Answer 2

Step-by-step explanation:

In mathematics, a rose or rhodonea curve is a sinusoid specified by either the cosine or sine functions with no angle that is plotted in polar . Rose curves or "rhodonea" were named by the Italian mathematician who studied them, between the years 1723 and 1728...

Hope its help...