# Definition:Boundary (Geometry)

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*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.