þrírvídd

þrírvídd is the Icelandic term for three-dimensional space, the geometric setting in which objects have length, width, and height. In mathematics and science it describes a space that can be specified by three independent coordinates, commonly labeled x, y, and z. This structure is modeled by Euclidean 3-space, denoted R^3, which forms a real vector space with a standard Euclidean metric.

Distances between points follow the Euclidean distance formula d = sqrt((Δx)^2 + (Δy)^2 + (Δz)^2). Vectors in þrírvídd can be added and scaled, with standard operations such as the dot product, which measures similarity of directions, and the cross product, which yields a vector orthogonal to a pair of vectors and relates to area and orientation.

Points and objects in þrírvídd are commonly described using Cartesian coordinates or alternative systems such as cylindrical or spherical coordinates. Transformations between coordinate systems are described by matrices and trigonometric relations. Three-dimensional geometry underpins many fields, including computer graphics, architecture, engineering, and robotics, where models, simulations, and animations operate in a virtual 3D space.

In physics, þrírvídd refers to the spatial dimensions in which physical processes occur, distinct from time, which is often treated as a separate dimension in the broader concept of spacetime.

This term is closely related to broader mathematical ideas about dimension and to practical technologies such as 3D modeling, printing, and virtual reality.