Definition:Boundary (Geometry)

This page is about Boundary in the context of Geometry. For other uses, see Boundary.

Definition

In the words of Euclid:

A boundary is that which is an extremity of anything.

(The Elements: Book $\text{I}$: Definition $13$)

For example, the endpoints of a line segment are its boundaries.

Containment

A geometric figure is said to be contained by its boundary or boundaries.

Notes

It can be intuitively perceived that the geometric and topological definitions of boundary are compatible.

Also see

• Boundary of Polygon is Topological Boundary