An octant is commonly defined several ways: first, as an antiquated tool for identifying angels and distances, and secondly, as a widely applied mathematical designation. In the field of general math, an octant is one of eight different regions created by a triple axis. This is easiest to see in a diagram where eight octants make up a three dimensional area or cube.
Beyond these two definitions, some professionals in the field of meteorology or astronomy use the word octant to refer to one of eight compass directions: North, Northwest, West, Southwest, South, Southeast, East, and Northeast. These are most often used as wind directions. An octant may be used when a simple wind directional signal is not sufficient to show how the wind is blowing.
In its use as a mathematical or spatial term, the octant doubles the two-dimensional quadrant. Mathematicians refer to the octant as the divisions of a Euclidean three dimensional system. The octant also comes with its own shorthand for designations, that often uses a set of three indicators within a set of parentheses, where plus and minus signs make up a designation for an octant. Although a "first octant" title distinguishes one of these eight sets, the others typically have no specific titles.
As an instrument for measuring, the octant was developed in the 1700s and used in navigation, where measures of the altitude of celestial bodies could show a latitude at sea. The octant, as well as the sextant, provided navigation assistance for navigation on many voyages over more than two centuries. Many attribute part of the origin of the octant to Isaac Newton's reflecting quadrant. Octants were made in a variety of materials, often using mirrors. As late as the 1950s, some navigators used a modern form called a bubble octant to find the horizon from above the earth.
As a conceptual math term, the octant has a wide range of applications. As mentioned, it is often used to divide space along an x-axis, a y-axis, and a z-axis, for the purposes of measuring or manipulating 3-D models, or for other kinds of projects where changes in a triple axis are important. As an alternative, some mathematicians also use an octant to refer to one eighth of a two dimensional circle. It has many uses in both its navigational and mathematical definitions, and remains a part of Euclidean reference today.