# A "Beautiful" Butterfly

by Preston Moore

This graph includes a variety of lines and equations including the lemniscate graph, rose graph, and circle graphs. By using them an image is created. I have created a beautiful butterfly because butterflies are free and can roam wherever they please. They have an added uniqueness to them on their wings, differentiating from one another making no two the same. This butterfly has 3 wings made from a rose graph and lemniscate graph. The body was created with the circle graph. Below are the equations making this possible

1) In order for this equation to come out the right way experimentation had to be done on the graph. For example, at first I had thought about making the wings on the butterfly with multiple circle graphs. However the circles didn't create the image that i was looking for. So instead I used the lemniscate graph so that the process would come out faster and easier. Instead the image looked just like a big blog cause there was too much overcrowding. They worked with the shape of the body. Finally I came up with the solution of using a 4 petal rose graph. It gave the image more of a realistic effect with it.

2) While I was completing the assignment I started to realize that most of the things I look at can be outlined with a simple line or circle. Shapes are all around us. No matter the size or the length anything can be recreated. I also started to notice that these equations associate with most of the problems we have to deal with while graphing lines like parallel and perpendicular lines.

3) At first this assignment was a challenge for me. The lesson turned out to be a challenge to graphs at first so coming up with the equations to fit with the lines and circles I had created wasn't so easy. Transferring information from document to document and sitting in front of the computer was a drag. But after I figured it out the rest of the assignment was a breeze.