Polar Rose Graph
name: Moses Yi
Phase 3 paragraph
The general structure of our design represents that of a flower inside of a vase. The inner part of the rose consists of a limnascate and a rose design; this is used to depict the inner part of the rose, specifically the stigma (graph 7&8). The next graph is an extended rose design, which represents the inner petals of the flower (graph 6). The four circles after the rose design, are used to create the outer petals of the flower in order to give the flower itself a larger look (graph 2,3,4,5). The final equation, is a large circle that surrounds the flower, representing the vase the the flower in inside of. (graph 1)
a) We experimented mathematically by finding different types, length, and size of the rose, lemniscate, and circle. To get a circle, the equation we used was r=n, where n = real number. After, we used the equation r= ncos(theta) or r = nsin(theta) to find a smaller circle either on the x-axis or y-axis, we could determine where it goes up, down, left, or right by making ncos(theta) and nsin(theta) negative or positive. To find the rose, we used the equation r=ncosp(theta), where p = the number of petals and when the number of petals is even, then we double the number. We know that in a rose graph that cos(theta) has one petal on the polar axis. After, we find the zeros of r. To find the lemniscate, we used the equation r^2= 2cos2(theta), to graph the lemniscate, we square root (r).
b) While we were completing this assignment, we learned how to identify the polar equation for each polar graphs. For example, equations for a circle, rose, and lemniscate. We learned how many rose petals we need to satisfy our needs, which is finding the number of petals. We also learned how to graph the equations that were made up and vice versa.
c) We enjoyed working on this assignment because it shows our creativity and liking of using equations to create a rose graph. This also helped us review on graphing the polar equations that we made, which helped us on the group quiz and test. This project was very exciting and was fun working with my partner.