# Definition:Geometric Figure

## Definition

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 $19$)

## Diameter

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**.

## Sources

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next):**figure**:**1 a.** - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**figure**:**1.**(**geometric figure**) - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**geometric figure** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**figure**:**1.**(**geometric figure**) - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**geometric figure** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**figure**(in geometry)