# Pre-Calculus Polar Graph Project (Flower Power)

### Brandon Sellens

My design depicts a central-based rose graph that represents a flower, which symbolizes non-violence and peaceful ways of reaching agreements. The lemniscate symbolizes an infinity sign, representing everlasting peace. The circle symbolizes a never-ending loop connecting us all as human beings. My design as a whole represents the 60's hippie movement, which embodied the ideas of working together toward an everlasting peace. The term "Flower Power," which is the title of my design, was a slogan from this era that reflects the peaceful, non-violent protests of the time period.

For my original sketch, I included a rose graph with 6 petals, but I had difficulty translating this to an equation.  If the number in front of the θ is an even number, then doubling this number tells how many petals there will be.  Following this idea, when working with 6 petals this number in front of the θ would be 3, however, the doubling rule cannot apply in this case because 3 is not an even number (the 3 would result in 3 petals being depicted on the graph).  Therefore, in Phase 2, I decided to change the number of petals in my design to 8 so that I could place the even number 4 in front of the θ in order to allow my equation to fit the rule, and to correctly correspond to the picture.  The new equation is r=5cos4θ.

a.) I thoroughly enjoyed this project because it gave me a chance to experiment mathematically with the various types of graphs I learned about in this chapter. I experimented mathematically particularly through Desmos - the graphing calculator website. Desmos presented me with a better understanding of my original graph. In my original, I had an equation that would have been too hard to translate to Desmos. Therefore, I changed up my equation to have it fit perfectly into Desmos. This altered equation occurred in the rose graph of my design which now reads r=5cos4θ from its original r=cos6θ.

b.) This assignment helped me study for the chapter test (Friday) considerably. By taking part in this project, I was able to become a specialist on every graph used in my design. This new found knowledge gave me the skills necessary to translate my work on tackk.com to the test last Friday. I learned that There are completely new types of graphs; graphed on an entirely new coordinate plane. Before this project, I was unaware that polar form even existed, but now I am quite the expert on both rectangular form and polar form.

c.) I really enjoyed working on this project because it felt like I was receiving the necessary knowledge to succeed come test time. I took my test today (5/12/2014) and felt very well prepared due to the practice I received while completing this project. I also feel it was very beneficial to get some new computer practice in on a web sight that was foreign to me as of 2 weeks ago. Thanks Ms. D