quadrant

A quadrant is a term used in several fields to denote one of four equal parts. In geometry, it refers to a quarter of a circle or of a plane divided by two perpendicular lines, typically the x- and y-axes. The Cartesian plane is divided into four quadrants: Quadrant I (x > 0, y > 0), Quadrant II (x < 0, y > 0), Quadrant III (x < 0, y < 0), and Quadrant IV (x > 0, y < 0). The first quadrant contains angles from 0 to 90 degrees, the second from 90 to 180, the third from 180 to 270, and the fourth from 270 to 360 degrees. The area of a circular quadrant is πr²/4 for a circle with radius r.

In anatomy, the abdomen is commonly divided into four quadrants by two perpendicular lines that intersect at the navel, creating the right upper, left upper, right lower, and left lower quadrants. This division helps describe the location of symptoms, organs, and findings in clinical practice.

Historically, a quadrant is also a navigational instrument used to measure angles in astronomy and navigation. The instrument is a quarter-circle arc equipped with sights and a plumb line, enabling observers to determine the altitude of celestial bodies relative to the horizon. It was widely used before being largely superseded by the sextant.

Etymologically, the term derives from Latin quadrans, meaning a quarter of a circle, from quadr- meaning four. The word is widely used across disciplines to denote one of four parts or regions.