My design is a rare flower with a four leaf clover blooming in the middle. I used a rose for the main flower, 2 lemniscates to make the four leaf clover, and 2 pole axes. The 2 pole axes are the "X" which portrays the flower as a treasure. In pirate terms, the "X" on the map marks where the treasure is located. This rare flower is considered a treasure because of its rareness.
a) In what ways did you experiment mathematically?
I experimented mathematically in many ways to create my "four leaf flower". First I figured out that to have a four leaf flower, I would need to have a "rose" graph to make the petals. Therefore, I used the rose equation, which is, r=9cos2(theta). A circle graph was used to support the petals. It is just the right size, r=9. Then, for the four leaf clover, I used 2 lemniscate graphs. I figured out that by using a negative equation (r=sqrt-16sin2(theta)), I would acquire the opposite of the other lemniscate graph making a four leaf clover. I figured that by using two poles, it would make the flower more lively.
b) What did you learn from doing this assignment?
During this assignment, I actually learned things that I did not know before. For example, I didn't know that you can make cool images just by using polar graphs. It's very interesting and amusing to me. Another thing I learned during this project was that it is possible to have a negative lemniscate equation to make the opposite. I used the negative equation to make half of my four leaf clover. Lastly, I learned the difference between a rose graph that is a sine and a rose graph that is a cosine.
c) Did you enjoy working on this assignment? Why or why not?
Surprisingly, I enjoyed working on this assignment. I found this to be a really fun assignment because I got to experiment with different equations to form a vivid image. While I enjoyed working, I also like the fact that I actually learned new things. Although I worked on this project by myself, it helped me become more independent.