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.
+ 
+ 
+ 
= 
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.