Overview

"Adjacent" is an adjective that describes something lying next to or near something else. In ordinary speech it denotes proximity or immediate neighborhood — for example, two rooms that share a wall are adjacent. The word is commonly used across disciplines to indicate a direct nearness or connection without intervening elements. In many technical contexts the term acquires a precise meaning tied to the objects being compared.

Mathematics and geometry

In geometry the word describes elements that meet or lie side-by-side. Two sides of a polygon that share a vertex are adjacent sides, and two angles that share a common side are adjacent angles; both definitions emphasize the shared boundary. Adjacency is also used for vertices and faces that touch each other.

Trigonometry and right triangles

In trigonometry the term appears in the phrase "adjacent side" of a right triangle. For a given non-right angle, the adjacent side is the side that touches that angle but is not the hypotenuse. That relationship underlies basic trigonometric ratios such as cosine, often expressed as cos(θ) = adjacent/hypotenuse. The notion ties a geometric position to numeric ratios used in calculations.

Other fields and everyday examples

Outside pure mathematics, "adjacent" appears in graph theory to indicate an edge joining two vertices (they are adjacent if connected by an edge), in computing as an adjacency matrix or list, and in real estate or urban planning to describe neighboring parcels or buildings. Common examples include adjacent seats in a theater, adjacent keys on a keyboard, or adjacent stations on a transit line.

  • Synonyms: nearby, adjoining, neighboring — though each carries slightly different connotations.
  • Contrast: "adjacent" usually implies immediate nearness rather than a loose association. In graphs, adjacency means connection even when no spatial notion exists.
  • Language note: The everyday sense of "next to" is often captured by the phrase next to, but technical definitions may be narrower.

For concise explanations focused on angles and polygon sides see articles about angles, and for triangle-side terminology consult resources on the right triangle. For algorithmic uses, references about adjacency structures in computer science are useful as an introduction.