Definition:Single Cusp

Definition

A single cusp is a cusp in which the curve is not continuous through the point.

That is, $2$ or more parts of the curve meet at a single point.

Single Cusp of the First Kind

A single cusp of the first kind is a single cusp in which both parts of the curve lie on opposite sides of the coincident tangents defining that single cusp.

Single Cusp of the Second Kind

A single cusp of the second kind is a single cusp in which both parts of the curve lie on the same side of the coincident tangents defining that single cusp.

Also see

• Definition:Double Cusp

• Results about single 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)