octant

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (December 2009)

Three axial planes (x=0, y=0, z=0) divide space into eight equal octant domains, each with a coordinate signs from (-,-,-) to (+,+,+).

An octant is one of eight divisions.

Octant in the plane

An 8-point windrose

Traditionally wind direction is given as one of the 8 octants (N, NE, E, SE, S, SW, W, NW) because that is more accurate than merely giving one of the 4 quadrants, and the wind vane typically does not have enough accuracy to bother with more precise indication.

Octant in three-dimensional space

An octant is one of the eight divisions of a Euclidean three-dimensional coordinate system defined by the signs of the coordinates. It is similar to the two-dimensional quadrant and the one-dimensional ray.^[1]

Usually, the octant with all three positive coordinates is referred to as the first octant. There is no generally used naming convention for the other seven octants.

• first octant (+, +, +)
• top-back-right (−, +, +)
• top-back-left (−, −, +)
• top-front-left (+, −, +)
• bottom-front-left (+, −, −)
• bottom-back-left (−, −, −)
• bottom-back-right (−, +, −)
• bottom-front-right (+, +, −)

Multi-dimensional space

The multi-dimensional generalization of the octant is the orthant, also called hyperoctant. An n-dimensional space is divided into 2ⁿ hyperoctants.

References