Some of the best signs of truly learning a topic is to translate the lesson into something new and be sure to have some room for fun and creativity. That is exactly what Mrs. Elking’s PreCalc class experienced with their recent project creating art out of polar graphs. In their practical use, the polar coordinate system, shown by polar graphs, is used in many fields, including mathematics, physics, engineering, navigation, and robotics. However, for this assignment, these graphs featured a number of creative designs through a variety of equations and point intersections resulting in some beautiful final results.
Mrs. Elking challenged her class to create original polar graphs that when finished, displayed a picture or an interesting design. Each graph needed to include:
- conic sections (ellipse, parabola, or hyperbola) in the form r = p/a+bcos θ or r = p/a+bsin θ
- Circle (not centered at the pole)
- A rose
- A limacon
- Line (horizontal, vertical and slanted)
- One additional graph that is rotated.
With those parameters in mind, the class took off and created numerous graphs. The finished projects included a bear, a full-colored frog, a sand dollar, and a turtle just to name a few!