Rose Petal Polar Plot With 6 Petals

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Bashyboy
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What is the functional form of rose petal with 6 petals? I am asked to graph this function with matlab, but it seems impossible according to my calculus textbook. According to my textbook, a rose curve can have the form [itex]r = a \cos n \theta[/itex] or [itex]r = a \sin n \theta[/itex]. When n is even, then there are 2n petals; when n is odd, then there are n petals.

Is there any way of accomplishing this, graphing a rose petal with 6 petals?
 
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Bashyboy said:
What is the functional form of rose petal with 6 petals? I am asked to graph this function with matlab, but it seems impossible according to my calculus textbook. According to my textbook, a rose curve can have the form [itex]r = a \cos n \theta[/itex] or [itex]r = a \sin n \theta[/itex]. When n is even, then there are 2n petals; when n is odd, then there are n petals.

Is there any way of accomplishing this, graphing a rose petal with 6 petals?

Experiment with nonintegers. Try n=3/2.
 
I shall assume you are edicted to pick n as an integer.
Let r = sin(nθ), and write α = π/n. The first petal is from θ=0 to θ=α, the second from α to 2α. But if you look at where these appear, the second will look like the first rotated about the origin by an angle - what angle (as a multiple of α)?
The third petal will look like the second, but rotated by that same angle. What will the total of these angles be when you stop getting new petals?
 
You can make a six-petaled rose with the equation ##r^2 = 3sin(2θ)##. I am not sure if the 3 changes the number of petals. But that will do it for you.
 
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simpsonsruler said:
You can make a six-petaled rose with the equation ##r^2 = 3sin(2θ)##. I am not sure if the 3 changes the number of petals. But that will do it for you.
No, that is a two petaled lemniscate.

Depending on your taste, you might try ##r=\sqrt{sin(6\theta)}## or you might try ##r = sin(3\theta/2)##. Those each have 6 petals, but the width of each petal is not ##(2\pi)/6## the way you might like.