Cycloidal geometry. Historical artwork showing a geometrical curve called a cycloid. This curve can be generated by tracing the path of a point on a circle that is rolling along a straight line. This can be seen as combining translational (forward) movement, and rotational (cyclical) movement. The shapes formed can vary, depending on the location of the point chosen, and the reference system used. An observer on the wagon sees only circular motions. A stationary observer will see cycloidal motion. This cycloid contains loops, and is called a prolate cycloid. Cycloids are used in the shape of gear teeth and violins. Artwork from Physique Populaire (E. Desbeaux, 1891).