Ya' Gotta Love Parametric Equations

Assigned November 4, 1998
Due December 9, 1998

This goal of this project is very simple: You are to use parametric and polar plots to create a drawing in Maple.

For example, try the following in a Maple worksheet:

              [> with(plots):
              [> p1 := polarplot(5+sin(3*theta),theta = 0 .. 2*Pi,color = violet,
                    scaling = constrained):
              [> p2 := plot([2*cos(t), -1+2*sin(t), t = 5*Pi/4 .. 7*Pi/4],
                    color = red):
              [> p3 := plot([-2+.8*cos(t), 2+.6*sin(t), t = 0 .. 2*Pi],color = blue):
              [> p4 := plot([2+.8*cos(t), 2+.6*sin(t), t = 8*Pi/7 .. 13*Pi/7],
                    color = blue):
              [> display(p1,p2,p3,p4);
              

A couple of comments:

• The colon at the end of the commands is very important. It prevents Maple from printing out the plot structure each time. If you forget it once, you'll see what I mean.
• You should make sure that at least one of your plots contains the option scaling=constrained. This will keep Maple from scaling your plots differently in the x and y directions.
• You should use at least 50 different functions in your final image.
• The more creative you are with this, the better your grade will be. For example, just lines, circles and ellipses would not earn you a high grade.
• Section 4.1 from the text has some information on combining linear and circular motion to get more interesting shapes. We'll talk about this in a couple of weeks.
• For those of you who have had linear algebra, you know how to stretch, skew, and rotate via matrix multiplication. This gives you and easy way to manipulate any parametric plot. If you haven't had linear, ask me (or someone who has had linear) and we can explain it to you pretty quickly.
• FIRST DRAFT DUE NOVEMBER 23: You should turn in a hand-drawn sketch of your final project and also a print out of your Maple worksheet containing a rough idea of your image (with at least five functions). This will count for 5% of your project grade.
• We'll have show-and-tell at the end of the semester where everyone can see each other's projects.
• Finally, HAVE A LOT OF FUN WITH THIS!!!!