This picture has 3 types of graphs. We did not make any changes from the phase 1. r=9 is a circle graph and it is the outer structure of the flower. R=9cos2theta is a rose graph and the petals of the flower. R=2 and r=2cos2theta is a circle and a rose graph. They are both inner parts of the flower. X=2 is the stems of the flower.
We experimented mathematically when we were drawing the graphs at first. At first, we did not know much about the graphs. So we drew graphs that did not exist. This experience gave us a chance to know how cosine and sine graphs are different for lemniscate, even petals double for the rose graph and also we could make all different sizes with the graphs. This project helped us to understand math in a fun way.
While we were completing this assignment, it showed that mathematical graphs can form different shapes. We thought the graphs could only create certain types of picture. However, it could display so many other pictures. Also it helped us to know exactly about polar graphs. Before this project, we had an hard time drawing a graph. But as we used desmos and drew so many different graphs, we mastered it. Especially the rose graph came easier to us.
We did not enjoy this assignment at first because we did not have any idea of how to graph. We could only think of graphs as just math. However, we started to gain more ideas and realize that several graphs can actually form beautiful picture. We think it was a memorable project due to the collaboration between math and art.