Octant

# Octant

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Encyclopedia
An octant is one of eight divisions.

## Octant in the plane

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
Euclidean geometry
Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions from these...

three-dimensional coordinate system
Cartesian coordinate system
A Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length...

defined by the signs of the coordinates. It is similar to the two-dimensional quadrant and the one-dimensional ray.

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
Orthant
In geometry, an orthant or hyperoctant is the analogue in n-dimensional Euclidean space of a quadrant in the plane or an octant in three dimensions....

, also called hyperoctant. An n-dimensional space is divided into 2n hyperoctants.