éndimensjonal

éndimensional is a term used in geometry and related fields to describe objects that require exactly one coordinate or parameter to specify a point on them. It denotes one dimension, in contrast to two-dimensional or three-dimensional spaces.

In mathematics, a one-dimensional object can be a line, a curve, or a one-dimensional manifold. Points on such objects can be described using a single parameter. For example, a straight line in the plane can be written as r(t) = p + t v with t real, where p is a point on the line and v is a direction vector. A circle is also one-dimensional, and it can be parameterized by r(θ) = (cos θ, sin θ) with θ in [0, 2π). These objects have the property that locally they resemble a line, even if they are embedded in a higher-dimensional space.

The ambient space in which a one-dimensional object exists may be higher dimensional. A 1D curve embedded in three-dimensional space retains its intrinsic one-dimensional character, while the surrounding space has three dimensions. This distinction between intrinsic dimension and the dimension of the surrounding space is common in topology and geometry.

In practical terms, ér-dimensional concepts appear in various contexts: in physics and engineering, as models of phenomena along a line or filament; and in computer science and data analysis, where a one-dimensional array or vector is a sequence indexed by a single coordinate. The term is related to higher-dimensional descriptions, such as two-dimensional (2D) and three-dimensional (3D) spaces, and to the general notion of dimensionality used to classify geometric and physical objects.