axes

Axes are lines used as reference points for measurement, rotation, and symmetry. In mathematics, a set of axes forms a coordinate system that locates points in space.

In two dimensions, the common axes are the x-axis and y-axis, intersecting at the origin. In three dimensions, the z-axis is added, and points are specified by three coordinates (x, y, z). Axes can extend to higher dimensions in abstract mathematics, where they provide orientations and reference directions for coordinates, vectors, and functions.

Axes serve several roles. The axis of rotation is the line around which an object spins. The axis of symmetry is a line that a figure can mirror across. In physics and engineering, principal axes align with directions of symmetry or inertia, and in linear algebra, eigenvectors define principal axes for certain matrices or quadratic forms.

In graphs and charts, axes frame the plotting area and determine how data are scaled and labeled. Horizontal axes are often referred to as the x-axis and vertical axes as the y-axis, with the third dimension represented by the z-axis in 3D plots. In machinery, an axis is a shaft or spindle around which a component rotates.

The plural form axes is the standard usage for multiple reference lines. The term derives from axis, with roots in Latin, and is distinct from the similarly spelled tool axe, though historically the words share a common origin.