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 which can be 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.
Also see
- Results about geometric figures can be found here.
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)