dimensjoner

Dimensjoner is the term used to describe the number of independent coordinates or parameters needed to specify a position or state of a system. In mathematics it is a formal property of a space or object, indicating its degrees of freedom. In everyday language the word can also refer to the size or extent of something. In Norwegian, dimensjoner is the plural form of dimensjon.

Examples help illustrate the concept: a point has 0 dimensions, a line has 1, a plane has 2, and ordinary three-dimensional space has 3. In physics, time is often treated as a fourth dimension, forming spacetime in Einstein's relativity. Some theories propose additional dimensions beyond the familiar four, usually compactified or hidden from direct observation.

Mathematics distinguishes several notions of dimension: topological, covering, and intrinsic versus extrinsic dimensions; fractal dimensions such as the Hausdorff dimension measure how a set fills space and can be non-integer. Dimensions can be integers or non-integers depending on the context. Dimensional analysis uses units to check physical equations by ensuring consistency of dimensions across terms.

In data science and computer graphics, the number of features or coordinates is referred to as the data dimension or the dimension of a space. Reducing dimensions is a common technique to simplify problems while preserving essential structure, for example by principal component analysis. The concept of dimensjoner thus connects geometry, physics, and information across disciplines.