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Mathematical Experiment 2

Construct the **rose curve** given by the equation in **polar coordinates**
r = cos 3t
Create an animation formed by rotating this curve with respect to the center.

Construct the **Bowditch curve** given by the **parametric equations**
x = cos 5t
y = cos 6t
Create an animation as this:

In this drawing:
what are the coordinates of the point G?

Show that a variable point on the line segment can be expressed as
H = (cos^{2}s cos t, sin^{2}s sin t) for some s.
Construct an animation showing that the astroid is tangent to a family
of ellipses, the sum of whose axes is constant.

Construct an animation showing the various positions of the **Trammel
of Archimedes.**

Construct an animation displaying the formation of the **astroid** as
a hypocycloid.

Construct the formation of the **ellipse** according to the parametric
equations

x = cos t
y = (sin t)/3