Double Point

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 also sometimes known as a node.

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

See also

Crunode, Cusp, Gauss's Double Point Theorem, Isolated Singularity, Ordinary Double Point, Quadruple Point, Rational Double Point, Spinode, Tacnode, Triple Point

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Aicardi, F. Appendix to "Plane Curves, Their Invariants, Perestroikas, and Classifications." In Singularities & Bifurcations (Ed. V. I. Arnold). Providence, RI: Amer. Math. Soc., pp. 80-91, 1994.Fischer, G. (Ed.). Mathematische Modelle aus den Sammlungen von Universitäten und Museen, Kommentarband. Braunschweig, Germany: Vieweg, pp. 12-13, 1986.

Referenced on Wolfram|Alpha

Double Point

Cite this as:

Weisstein, Eric W. "Double Point." From MathWorld--A Wolfram Web Resource.

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