sluttpunkter

Sluttpunkter, or endpoints, refer to the points at which an object such as a geometric figure or a curve begins or ends. The concept is used across mathematics and related fields, and its precise meaning depends on the context.

In geometry, a line segment has two endpoints, while a ray has one endpoint. A circle or any closed curve has no endpoints since it has no distinct start or end. An open arc or an open curve has endpoints at its ends. The endpoint concept helps distinguish between finite and infinite or open versus closed structures.

In the setting of curves and functions, a parameterized curve γ: [a,b] → R^n has endpoints γ(a) and γ(b). If γ(a) = γ(b), the curve is closed and, by the usual definition, has no endpoints. Endpoints of a curve are often important for defining attributes like length, continuity, or boundary behavior.

In graph theory, endpoints (often called leaves) are vertices of degree 1 on a graph, and they correspond to the ends of a path or a tree. Endpoints are useful for understanding the shape and structure of networks, such as road systems, river graphs, or data trees.

End points are sometimes distinguished from boundary points. A boundary point lies on the boundary of a set in a topological sense, but not every boundary point is an endpoint of a particular object embedded in the space. The endpoint concept is thus object-relative and depends on how the object is defined.

Examples include the endpoints of the segment from (0,0) to (1,1), which are (0,0) and (1,1). A circle has no endpoints. In a simple graph path with three edges, the end vertices are the endpoints and have degree 1.