Grace Yoo & Alice Park
For our graph, we changed the lemniscate graph to r^2=64cos2thetha. The lemniscate from phase 1 is not an existing graph for there is no lemniscate that has a theta=pie/2 symmetry. From changing this, you can see the difference it makes when entered into desmos. From phase 1 and phase 2, we did not realize how that the rose only had 3 petals instead of 4 for the equation only states that there are 3 petals.
We experimneted mathematically when we tried out which graphs worked and which didn't work. We also experimented by entering different formulas on Desmos and made sure the graphs we chose were the ones that completed our project. By trying out different formulas to get the graph we needed, we were able to learn which graphs exist and which don't.
While were were completing this assignment, we learned that there is no existing lemniscate graph with a symmetry of theta=pie/2. When a cos lemniscate is graphed, it is placed along the x-axis so we assumed that when we graphed a sin lemniscate, it would align on the y-axis. Instead, it turned out to be more slanted with a pole symmetry.
I honestly did not enjoy working on this project because it was very hard to work with my partner because we were bothy very busy studying for upcoming finals and AP tests. On top of that, we could never really communicate about our project because we were too busy with basketball and cheer and tutors, which made it even more difficult to perfect our project.
Mathematically, we experimented different types of graph forms in order to make a design on desmos. We ended up using the circle, lemniscate, and rose graphs. We continually changed the length and number of petals in the rose graph and attempted various types of graph designs. Eventually, we created the graph we were satisfied with.
While Grace and I were completing this assignment, we learned how to use the tackk application website and learned how to graph complex shapes on Desmos. We learned that a lemniscate cannot run along the y-axis with a symmetry of theta=pi/2.
This project helped me understand a little more of the different aspects of the complex graphs of the lemniscate and rose. However, this project would have been more enjoyable if it were at a separate time, apart from all the APs and finals testing. Numerous times along the way, we were unclear of some instructions as well. Overall, however, this was a manageable project.