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Geometric Construction 8

Construct an animation displaying various equilateral triangles whose sides
are tangent to the cardioid. The number of solutions is > 1.

Construct an animation displaying a rigid nephroid passing through the
vertices of a stationary equilateral triangle.

Construct an animation displaying a rigid astroid passing through the vertices
of a stationary equilateral triangle.

Construct the gear-wheel coupling of epicycloids and hypocycoids.

Construct the gear-wheel coupling of epitrochoids and hypotrochoids.