Construct · 1 fields · 2 citations

cusp: a standalone construct

One name. One construct. A landmark on the map.

● anchor · a standalone construct Nearest construct by meaningtangentcompare the meanings
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cusp1 CONSTRUCTCurve cuspNEWTON · CURVE CUSP

A single standalone construct; nearby constructs are located against it in the Collider. Tap a field for its definition, unit, and measures.

Mathematics

A singular point where a curve reverses

In his 1704 Enumeratio linearum tertii ordinis, Newton classified the cubic curves and the special points at which a curve can fail to be smooth, among them the cusp: a point where two branches of the curve meet, share a single tangent line, and the direction of travel along the curve reverses. There the curve comes to a sharp beak instead of passing through smoothly, so the tangent direction is undefined. The same shape reappears in Zeeman's 1976 account of the cusp catastrophe, where a smooth control surface folds so that its edge traces a cusp. The referent is an abstract feature of a curve or surface, defined by calculus, not a horn of light on the Moon or a raised part of a tooth or valve.[1][2]

Unit
One singular point on a curve, described by how its branches and tangent behave
Recovery means
Not applicable
Measured by
Identified analytically where the derivatives vanish so the tangent direction is undefined, or seen as a sharp reversal in the plotted curve

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Nearby constructs

tangent3 fields · 5 citationsjingle · one word, three constructsvalve1 fields · 1 citationsanchor · a standalone constructsingularity3 fields · 5 citationsjingle · one word, three constructs

References

  1. Newton, I. (1704). Enumeratio linearum tertii ordinis. In Opticks. Sam. Smith & Benj. Walford.
  2. Zeeman, E. C. (1976). Catastrophe theory. Scientific American, 234(4), 65–83. https://doi.org/10.1038/scientificamerican0476-65

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