- a place on a curve from which there are two main tangents (given that it touches itself, or has actually a cusp)
- a point of a curve from which two limbs cross each other. Conjugate or separated things of a curve are known as two fold things, because they possess a lot of the properties of dual points (see Conjugate). Also called acnodes, and those things where in fact the limbs of this bend truly mix are called crunodes. The extremity of a cusp is also a double point.