Definition:Geometric Figure

From ProofWiki
Jump to: navigation, search


A geometric figure is intuitively defined as a set of points and lines in space.

In the words of Euclid:

A figure is that which is contained by any boundary or boundaries.

(The Elements: Book $\text{I}$: Definition $14$)

The boundary may or may not be included in a particular figure. If this is important (and in the study of topology it usually is), then whether it is included or not needs to be specified.

Plane Figure

A plane figure is a geometric figure embedded in the plane.

Three-Dimensional Figure

A three-dimensional figure is a geometric figure which cannot be embedded in the plane, but which can be embedded in three-dimensional space.

Rectilineal Figure

In the words of Euclid:

Rectilineal figures are those which are contained by straight lines, trilateral figures being those contained by three, quadrilateral those contained by four, and multi-lateral those contained by more than four straight lines.

(The Elements: Book $\text{I}$: Definition $19$)


The diameter of a geometric figure is the greatest length that can be formed between two opposite parallel straight lines that can be drawn tangent to its boundary.

Also known as

A geometric figure is also known colloquially as a shape.