Definition:Double Cusp
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Definition
A double cusp is a cusp in which $2$ or more parts of the curve are both continuous through the point.
That is, the curve is tangential to itself.
Double Cusp of the First Kind
A double cusp of the first kind is a double cusp in which both parts of the curve lie on opposite sides of the coincident tangents defining that double cusp.
Double Cusp of the Second Kind
A double cusp of the second kind is a double cusp in which both parts of the curve lie on the same side of the coincident tangents defining that double cusp.
Point of Osculoinflection
A point of osculoinflection is a double cusp in which one or both parts of the curve has a point of inflection at the point of contact with the tangents defining that double cusp.
Also known as
A double cusp is also known as a tacnode or an osculation.
Also see
- Results about double cusps can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): cusp (spinode)
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): double cusp
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): cusp (spinode)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): double cusp