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 a =1, b =1, k =2 a =1, b =1, k =3 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 b =1, k =2 b =1, k =3 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 b =1, k =2 b =1, k =3 b =1, k =4

And an animation letting k vary from 0 to 20:

Let's put them all together to compare:

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