Selftangency

Selftangency is a term used in geometry to describe a curve or surface that intersects itself in a way that is tangent to itself. This means that at the point of self-intersection, the curve or surface does not cross over itself but instead touches itself and "bounces back" along the same direction it arrived from.

Imagine drawing a loop on a piece of paper. If you draw a simple oval, the curve does not intersect itself. However, if you were to draw a figure-eight shape, the point where the two loops meet is a self-intersection. If, at that meeting point, the curve were to smoothly transition without crossing, it would be a selftangent point.

Selftangency can occur in various geometric contexts. For instance, in the study of algebraic curves, a curve can have a point of selftangency. Similarly, surfaces in three-dimensional space can exhibit selftangency.

The mathematical analysis of selftangency involves understanding the derivatives of the curve or surface at the point of intersection. A point is considered selftangent if the tangent vector to the curve or surface at that point is the same for both "sides" of the intersection. This distinguishes it from a simple transversal intersection where the curve or surface crosses itself. Selftangency implies a smooth continuation of the geometric object.