Line (geometry)

A line is one of the most fundamental objects in geometry: a straight, one-dimensional path extending infinitely in both directions. Unlike a line segment (which has two endpoints), a true geometric line has no beginning or end. It is defined by any two distinct points, and those points alone determine it uniquely.

Lines form the backbone of geometric reasoning. They are the basis for polyhedra, appear in Navigation and Demographic mapping, and underpin the calculus used to measure curves and areas. In analytic geometry, lines are expressed as equations—the simplest being y = mx + b in two dimensions, where the slope m and intercept b fully describe the line's behavior.

Beyond Euclidean space, lines take on new meanings: in abstract algebra, they model relationships; in physics, they trace trajectories. The concept is so essential that non-Euclidean geometries (like those on spheres) redefine "line" as a geodesic, the shortest path between two points on a curved surface.

Lines are invisible yet everywhere—in architecture, art, social networks, and nature itself.

Related

Plane (geometry), Point (geometry), Angle, Parallel lines, Coordinate system, Euclidean geometry