What is the first octant?

In the context of solid three-dimensional geometry, the first octant is the portion under an xyz-axis where all three variables are positive values. Under a Euclidean three-dimensional coordinate system, the first octant is one of the eight divisions determined by the signs of coordinates.

In a Euclidean three-dimensional coordinate system, the first octant is generally located in the top-front-right quadrant and is the only octant where every variable is positive. The seventh octant, located in bottom-back-left quadrant, is a portion under the xyz-axis where all three variables are negative values. The other six octant divisions can have one or two positive variables.