Definition:Boundary (Geometry)

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


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.


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


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

Also see