1dimensional

1dimensional, commonly written as one-dimensional or 1D, refers to spaces or systems that vary along a single independent coordinate. In mathematics, a prototypical example is the real line, consisting of all real numbers with distance given by the absolute difference. Such spaces are called one-dimensional and are among the simplest nontrivial manifolds after zero dimensions.

In mathematical terms, a one-dimensional space has dimension one: locally it resembles a line; a one-dimensional vector space is any line through the origin. The standard metric is d(x,y) = |x − y|, and the space is topologically equivalent to the real numbers. More generally, any curve that can be parametrized by a single parameter is one-dimensional.

Applications and physics often model processes confined to a line. Examples include a particle in a one-dimensional potential, waves on a string, and electronic states in a linear chain of atoms (tight-binding model). One-dimensional models are used to gain analytic insight and to illustrate concepts that extend to higher dimensions.

Limitations include the fact that real objects have width and volume, so true physical space is three-dimensional; one-dimensional models are idealizations that simplify analysis. In computer science, 1D can refer to data structures such as arrays or sequences indexed by a single coordinate; higher-dimensional data structures use matrices or tensors.

Terminology: while 1dimensional appears in some contexts, formal writing typically uses 1D or one-dimensional. The term is sometimes encountered in programming, naming conventions, or informal descriptions where a single coordinate is emphasized.