Final Project Must Include the Following

Polar Project

This assignment is to mess around with polar functions and find a shape that is really interesting to you. I want you to give your shape a name* and figure it out. Find all of the rules that govern your shape’s behavior and explain them. (For example, the shape is governed by the size of a and b in relation to each other. If a > b, then … happens. If a < b, then…happens, etc.) How does your shape change from sin to cos? Do you have to look at more than to see your whole graph? You can make a poster or a small book to explain your shape.

Final project must include the following:

• Named shape.
• One copy on a giant polar grid with a complete table of values. (Your shape may need a larger table than those we used in class.) If the shape varies greatly (limaçons with or without loops for example) you must show the variations on additional giant copies.
• Explanation of behavior. Your explanation should be clear to any person who has studied math at the precalculus or higher level. A reader should understand the intricacies of your shape, the way it is graphed, and the why behind those.

Grading: Make your final product interesting to look at and highly informative. Be creative, impress your friends, and wow me!

*There is a possibility that your shape already has a name, but we won’t worry about that. 

Some things to try out: Try messing with the …what if you do /2? What about /3? What if you multiply sin and cos? What if you put other operators into your function (square roots, absolute value, etc.)…what else can you do? Tan?

OR

Polar Graphing Art Project

For this project, your job is to create a work of art on a polar graph using polar equations. You must use at least 4 different polar equations and or including one equation not studied in class. The graphs will overlap, and by coloring the spaces between the curves creatively you will create a design that is interesting to look at. I will provide a large polar graph for your final project.

You will be given ONEgiant sheet of polar graph paper, so please be careful with it and do all sketch work elsewhere. The equations, their names, and their tables of values for () should all be neatly listed on the same sheet as the graph.