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Assignment 11

by

Allison McNeece


For this assignment we will be investigating the rose (or rhodenea) curve as a way of exploring graphs plotted with polar coordinates.


 

We will start by graphing the equation r =a + b*cos(kθ)

a =1, b =1, k =1

rose with a=1,b=1,k=1

a =1, b =1, k =2

rose with a=1,b=1,k=2

 

a =1, b =1, k =3

rose with a=1,b=1,k=3

a =1, b =1, k =4

rose with a=1,b=1,k=4

 

 

Hmmm... the name for this graph is starting to make sense. As the integer value for k changes "petals" form in our graph.

Below is an animation that allows k to vary from 0 to 20.

(With any of the animations you should be able to click or double click on the animation to pause or start the animation. Also if you have a scroll function on your mouse you can scroll through each frame while the animation is paused)


 

What if we took a out of the equation and use r = b*cos(kθ)?

 

b =1, k =1

rose with b=1,k=1

 

b =1, k =2

rose with b=1, k=1

b =1, k =3

rose with b=1,k=3

b =1, k =4

rose with b=1,k=4

Notice how in our first equation which included a the number of petals was k but when we took a out of the equation the number of petals is now 2k for even k.

Again let's look at an animation letting k vary from 0 to 20 we get:


 

Let's get real crazy and replace cosine with sine, giving us the equation r = b*sin(kθ)

b =1, k =1

sine rose with b=1, k=1

b =1, k =2

sine rose with b=1, k=2

b =1, k =3

sine rose with b=1, k=3

b =1, k =4

sine rose with b=1, k=4

 

And an animation letting k vary from 0 to 20:


 

Let's put them all together to compare:

equations for 3 graphs

a graph of the case where a=1, b=1, k=1

a graph with a=1,b=1,k=1

 

 


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