PHASE 1

"Sunflower" — Tiffany Le P.1 & Bianca Villaruel P.2

PHASE 2

Phase2 graph - "Sunflower" by Tiffany Le P1 & Bianca Villaruel P2

(NO CHANGES WERE MADE)

My partner and I designed our project to depict a "sunflower", in which each polar graph plays an essential part to the overall design. In our sunflower, there are 4 different polar graphs; graph #1 (r=1) is a circle which represents the bud of the sunflower. Graph #2 (r=2) is a slightly bigger circle that represents the outermost bud. Graph #3 (r=7sin5θ) is a rose which represents the petals of the sunflower that bloom out. And graph #4 (r^2=64sin2θ) is a lemniscate that represents the two leaves sprouting out underneath the petals of the sunflower. Each polar graph contributes to the overall design of the sunflower.

Graph #1- The inner circular bud of the sunflower (black colored)
Graph #2 - The outer circular bud of the sunflower (brown colored)
Graph #3 - The 5 petals of the sunflower (yellow colored)
Graph #4 - The 2 leaves supporting the sunflower (green colored)

PHASE 4 (SELF-REFLECTION)

Desmos graphs and equations for "Sunflower" by Tiffany Le P1 & Bianca Villaruel

We experimented mathematically when we began by creating a mesh of polar graphs that depicted a sunflower-like design. We first started off by adding 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 two leaf petals that compliment the overall design of the sunflower. Through trial and error, my partner and I designed a sunflower with four functional polar graphs.

While we were completing each step of the assignment, my partner and I learned many things. Mainly, we learned how to graph and find the equations of lemniscates, roses and circles. We also became familiar with the different aspects of each graph such as the symmetry of pole, polar axis and theta. Thanks to this project, my partner and I are now able to successfully graph polar equations and are capable of creating graphs through almost any equation. Lastly, we learned how to operate the functions of the desmos calculator where we are now able to navigate through the website easily and use this new gadget for future mathematical projects.

This project was interesting and helpful concerning the significance of graphs, regardless of how tedious it might have been. Completing this polar project was truly a insightful learning experience for we have learned many mathematical techniques that would help us in understanding the fundamental methods of graphing polar equations in pre-calculus. Now, my partner and I can proudly recommend this project to pre-calculus students who should take time to learn the crucial graphing skill they can use for their own benefits.