In geometry

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

, a supporting line L of a curve

Curve

In mathematics, a curve is, generally speaking, an object similar to a line but which is not required to be straight...

 C in the plane is a line that contains a point of C, but does not separate any two points of C. In other words, C lies completely in one of the two closed

Closed set

In geometry, topology, and related branches of mathematics, a closed set is a set whose complement is an open set. In a topological space, a closed set can be defined as a set which contains all its limit points...

 half-planes defined by L and has at least one point on L.

There can be many supporting lines for a curve at a given point. When a tangent exists at a given point, then it is the unique supporting line at this point, if it does not separate the curve.

The notion of supporting line is also discussed for planar shapes. In this case a supporting line may be defined as a line which has common points with the boundary of the shape, but not with its interior.

Two disjoint bounded planar shapes have four common lines of support. Two of them which separate the polygons are called critical support lines.