# Definition:Boundary (Geometry)

From ProofWiki

*This page is about boundaries in the context of geometry. For other uses, see Definition:Boundary.*

## Contents

## 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.