This applet demonstrates the principle of a "cycloid".
To try this
simulation:
Click on the flashing icon to select a type of wheel (Square or Round). Left-drag your mouse to rotate the applet.
What's Going On?
A square wheel would give you a smooth ride when moving across the surface of a cycloid. Conversely a point on a circular wheel traces a cycloid when it moves across a flat surface.
Mathematically the length of the cycloid arc is equal to 4 times the circle diameter with in that arc or 4 D. The side of each square wheel must be shorter than this in order for the square to roll smoothly. A square side must be as long as it is between the points that touch the ground. This is equal to 3.14159 times the circle diameter, or D.
