A plane curve which is progressively drawn. (Cycloid)

The Cycloid is the orbit of a point on a circle rolling along a straight line. Here you can see how this is done precisely, with multiple curve plotting.

By the same principle, the astroid (cos^3(t),sin^3(t)) is the orbit of a point on a circle of radius 1/4 rolling inside a fixed circle of radius 1.

We have also the astroid with 3 arcs.

Zooming effect on the curve sin(1/x).

A moving tangent along a plane parametric curve (cardioid).

The moving tangent along the astroid has a special property: the segment of the tangent cut out by the coordinate axes is of constant length.

How an ellipse is drawn by a point on a segment of fixed length with two extremities on the x and y axes respectively.

An animation which illustrates the functions sin and cos as vertical and horizontal positions of a moving point on a circle.

Rotating and growing trefoil.

Cornu Spiral - the Fresnel cosine and sine integrals.