spinode

Century Dictionary and Cyclopedia

1. n. In geometry, a stationary point or cusp on a curve. A spinode may be conceived as resulting from the vanishing of the angle at a node between the two branches. the length of arc between them being reduced to zero, just as an inflection may be regarded as resulting from the vanishing of the interval between the two points of tangency of a bitangent, the total curvature between them at the same time vanishing. But this view in the latter case includes all the points of the inflectional tangent as points of the curve, and in the former case includes all lines through the spinode as tangents. For this reason the spinode, like the inflection, is reckoned as a distinct kind of singularity. A curve cannot, while remaining real change continuously from having a crunode to having an acnode without passing through a form in which it has a spinode.