Octant

For other uses, see Octant (disambiguation).

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

1. ^ Weisstein, Eric W., "Octant" from MathWorld.