Distance

Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two counties over"). Since spatial cognition is a rich source of conceptual metaphors in human thought, the term is also frequently used metaphorically to mean a measurement of the amount of difference between two similar objects (such as statistical distance between probability distributions or edit distance between strings of text) or a degree of separation (as exemplified by distance between people in a social network). Most such notions of distance, both physical and metaphorical, are formalized in mathematics using the notion of a metric space. In the social sciences, distance can refer to a qualitative measurement of separation, such as social distance or psychological distance. The distance between physical locations can be defined in different ways in different contexts. Euclidean distance The distance between two points in physical space is the length of a straight line between them, which is the shortest possible path. This is the usual meaning of distance in classical physics, including Newtonian mechanics. Straight-line distance is formalized mathematically as the Euclidean distance in two- and three-dimensional space. In Euclidean geometry, the distance between two points A and B is often denoted . In coordinate geometry, Euclidean distance is computed using the Pythagorean theorem. The distance between points (x1, y1) and (x2, y2) in the plane is given by: Similarly, given points (x1, y1, z1) and (x2, y2, z2) in three-dimensional space, the distance between them is: This idea generalizes to higher-dimensional Euclidean spaces. Distance measurement There are many ways of measuring straight-line distances. For example, it can be done directly using a ruler, or indirectly with a radar (for long distances) or interferometry (for very short distances).