**"Eye" See You**

### Maddy DeLucca, Matt Chang

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We made multiple changes to our phase one graph in order to scale it to the smaller polar graph that was given in phase two. First, we changed the outer circle from r=10 to r=6. Next, we changed the inner circle from r=6 to r=5. We decided to make this circle smaller than it would be by just scaling it to the smaller graph. We did this in order to outline our lemniscate "eyes," which we changed from r^2=49cos(theta) to r^2=25cos(theta). Lastly, we changed our rose graphs accordingly. Our design is supposed to resemble something of Aztec or tribal artwork. The rose graphs were used to create a flower like, psychedelic background design, while the lemniscate graph creates our eyes. We decided to get rid of the black pupils we had in phase one since we could not actually graph them, being that they were only drawn for design purposes anyways. However, you can still tell the purpose of the lemniscate graph as eyes by its bright blue color, hence our title "Eye" See You.

While creating the design for our polar graph project we were inclined to experiment mathematically. We experimented mathematically mostly when creating the two overlapping rose graphs, forming the main psychedelic design of our project. We were required to experiment when figuring out the spacing between the petals of our second rose graph, in order to fill in the gaps of the first as we desired. To do this we had to go through a trial and error process when considering the number we would place in front of theta in our rose equation. To do so we divided 2pi by each trialing number until we got the closest spacing and look of our graph to how we had imagined it to be. Overall, graphing each rose graph, along with the lemniscate graph, were mathematical experiments in themselves. Being that these graphs are not so simply plotted as circles, nor as simple in general, it required experimentation when sketching. To say the least, the entire process of this project was one large mathematical experimentation.

While completing this assignment we learned a variety of valuable information. First and foremost, we learned a lot about writing equations. By creating our own graphs and then writing the equations after, instead of vise versa, we learned how the equations and their parts comply to our graphs. We gained a better understanding of how to write equations when just given a graph for reference as well. We learned how each part of the equation connects to our graphs, hence helping us to write equations in the future. We also learned, simply, to graph better; gaining a better understanding of what each graph looks like, and the difference between the sin and cos versions of a graph. We also learned the important difference of setting our equations equal to r^2 for lemniscate graphs, and just r for rose graphs-- being that we were slightly confused by the difference in the equations between the two graphs before this project. Both my partner and I learned a plethora of information when completing this assignment, while also gaining a much better valued understanding of things we had thought we already knew.

Overall, working on this project was an enjoyable experience. We enjoyed working on this assignment very much. Not only did it help us in preparing for our test, but it really helped us in gaining a long-lasting, better understanding of polar graphing and their equations. Also, using Tackk made the project different than most typical projects, adding to our enjoyment. The use of Tackk made the project more interesting and fun, and definitely of more ease. Working on our polar graph project was a very beneficial and enjoyable learning experience.