Have you ever played with a Spirograph toy? The one with the two circles? That toy uses the same math as the curves I used to draw these flowers! These hypotrochoid curves are drawn by one “set” circle that another “rolling” circle is moving along (an inner edge of both circles line up together). The curves are “drawn” by a point outside the moving circle at a set distance (d) and angle. For both of my curves, the rolling circle was larger than the stationary circle (unlike the Spirograph toy).
I wanted to do this project with flowers because I’ve always loved flowers and I am a huge plant person. I have five plants in my dorm! I also really enjoyed playing around with the hypotrochoid curves at the end of the second lab. For the project, I graphed two flowers. I started off by playing around with the different variables and just observing what changes happened in the graph. I would figure out a ratio of R and r that looked somewhat like the flower I wanted it to be and then kept adjusting it by smaller and smaller increments.
