A point traced out twice as a closed curve is traversed. The maximum number of double points for a nondegenerate Quartic Curve is three. An Ordinary Double Point is called a Node.

Arnold (1994) gives pictures of spherical and Plane Curves with up to five double points, as well as other curves.

**References**

Aicardi, F. Appendix to ``Plane Curves, Their Invariants, Perestroikas, and Classifications.'' In
*Singularities & Bifurcations* (V. I. Arnold). Providence, RI: Amer. Math. Soc., pp. 80-91, 1994.

Fischer, G. (Ed.). *Mathematical Models from the Collections of Universities and Museums.*
Braunschweig, Germany: Vieweg, pp. 12-13, 1986.

© 1996-9

1999-05-24