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 = (cos2s cos t, sin2s 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