zAchsen

zAchsen is the term used to refer to the z-axis in a three-dimensional Cartesian coordinate system. The z-axis represents the third dimension, commonly linked to depth or height depending on the convention. In most contexts, the x- and y-axes define a horizontal plane, while the z-axis is perpendicular to that plane.

Notation and orientation: A point in three-space is written as (x, y, z). The unit vector along the z-axis is often denoted as z-hat or k. In a right-handed coordinate system, x cross y equals z, but the direction of positive z varies by convention; some disciplines take z to point upward, others to point out of the screen or away from the viewer.

Applications: The z-axis is used across mathematics, physics, computer graphics, engineering, and GIS. In graphics, z-depth helps determine perspective and occlusion. In 3D printing, CNC machining, and robotics, motion along the z-axis controls vertical position or depth. In geography, z can denote elevation above a reference surface.

Terminology: In German-language sources, the axis is typically called Z-Achse (plural Z-Achsen). The concatenation zAchsen may appear as a stylistic label in some texts or databases, but standard terminology remains Z-Achse or z-axis.

See also: X-axis, Y-axis, Cartesian coordinate system, depth, elevation.