Joseph Lee, Timothy Yi

My design is a lily pad with a flower. The circle serves as the base of the lily pad and the rose petals and the orange colored lemniscate are the flower. The orange lemniscate indicates that the flower has bloomed. The two remaining lemniscates are placed there as a sign that the flower will continue to bloom, growing larger and larger with the petals growing more and more visible.

     To start off, we invested our time by experimenting in numerous ways in which we came to a final product. We initially started off by creating a circle graph that would be large enough to balance out in size with the other graphs creating a desirable proportion in relation to these other graphs. Next, we added in a rose graph and experimented with it by switching around the values of the rose graph to give it enough petals and length to look like a actual flower. Furthermore, to add on to the complexity of the flower we added lemniscate graphs and played around with the equations so we would come up with a flower that would closely resemble that of a lily pad. This is how we experimented with the project.

     While we were completing this assignment we learned many things. Overall we learned how to graph limacons, roses and circles. We also became familiar with the different aspects of each graph such as pole, polar axis and theta symmetry. From this project we are now able to successfully graph these graphs and we are now capable of creating desired graphs using equations. One of the last things we learned was gaining a familiarity with the desmos calculator in which we are able to navigate through the website, creating graphs with ease.

     Although working through this project was rather tedious, we still enjoyed working on it. Our reasoning behind this was that completing this project was truly a insightful learning experience for we learned many mathematical techniques that would help us in both pre-calculus and calculus. After completing such a project  definitely recommend assigning it to students who are planning to partake in the pre-calculus course mainly due to the crucial graphing skill they can potentially obtain after completing it.

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