How do vectors help you find formulas
for curves that are built up as combinations of simple motions?
More specifically, what were the
simple motions that generate roulettes? How did you combine their vector representations?
You used an applet simulation
of the Spirograph® toy to draw cardioids and other epicycloids.
Can these curves be drawn with a real Spirograph®? (If
you're not sure, consult the picture in Part 2.) Explain your answer.
The figure below shows the curve
used to make the design on our title page. What can you conclude about the
relative sizes of a, b, and c for this figure?
(Optional) What (if anything)
did you have to change in the formulas to go from curves generated by rolling
on the outside of the fixed circle to curves generated by rolling on the inside?
(Optional) Can a real Spirograph®
draw a hypocycloid? (See question 3.)
