Plane (mathematics)

A plane is a perfectly flat surface extending in all directions. It can be thought of as the ceiling of a room, only extended into all directions infinitely. A plane has two dimensions: length and width. All planes are flat surfaces. If a surface is not flat, it is called a curved surface.

The tool plane can be used to create a flat, level surface like the mathematical plane—hence the name.

In geometry, a plane is made up of an infinite number of lines (or points). It has no depth. It is absolutely flat and infinitely large.^[1]

A plane figure is part of a plane. It is named by the capital letters (such as A, B, C, ...X, Y, Z) that are put at its corners. Sometimes, a single capital pi ${\displaystyle \Pi }$ is also used to refer to a plane.^[2] A plane can also be named after three points that are not all on the same line.^[3]

In general, two planes can be:

• Parallel (they never meet)
• Concurrent (they meet forming a line)
• Coincident (they are one and the same)

1. ↑ "Introduction to plane geometry - Math Open Reference". www.mathopenref.com. Retrieved 2020-09-24.
2. ↑ "List of Geometry and Trigonometry Symbols". Math Vault. 2020-04-17. Retrieved 2020-09-24.
3. ↑ "An introduction to geometry (Geometry, Points, Lines, Planes and Angles)". Mathplanet. Archived from the original on 2020-09-29. Retrieved 2020-09-24.