Definition:Cusp
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Definition
A cusp is a singular point on a curve at which there are two different tangents which coincide.
Thus a cusp is a special case of a double point in which the tangents are coincident.
Cusp of the First Kind
A cusp of the first kind is a cusp in which both parts of the curve lie on opposite sides of the coincident tangents defining that cusp.
Cusp of the Second Kind
A cusp of the second kind is a cusp in which both parts of the curve lie on the same side of the coincident tangents defining that cusp.
Also known as
A cusp is also known as a spinode.
Examples
Also see
- Results about cusps can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): cusp (spinode)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): cusp (spinode)