1Dfiguren

1Dfiguren is a term used for geometric figures confined to one dimension. In mathematics, these figures are subsets of a one-dimensional affine space, most commonly the real line. The simplest nonempty 1D figure is a point. The next are intervals: closed [a,b], open (a,b), and half-open [a,b). Unbounded intervals such as [a, ∞) and (−∞, b] extend without bound in one direction. The finite line segment [a,b] is a basic 1Dfigure and consists of all points x with a ≤ x ≤ b. A line, if allowed, can be considered an unbounded 1D figure with no endpoints, while rays extend from a starting point to infinity.

Properties: The length or size of a finite 1D figure is the difference of its endpoints, b−a. The distance between two points x and y on the line is |x−y|. Intersections and unions of 1Dfiguren follow interval arithmetic: intersections of intervals are again intervals or empty; unions of disjoint intervals form a finite or countable set of intervals.

Notation and representation: A 1Dfigur is described by endpoints (a,b) or by inequality constraints. Orientation can be defined if needed, but geometric properties do not depend on orientation.

Applications: One-dimensional figures model segments of motion, time intervals in scheduling, and discrete geometry problems. They underpin algorithms for interval scheduling, search, and line sweep methods in computational geometry.

See also: real line, interval, line segment, ray, point, metric space.