Екі нүктенің арақашықтығы

Separation between two points

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.

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: For example, psychological distance is "the different ways in which an object might be removed from" the self along dimensions such as "time, space, social distance, and hypotheticality". In sociology, social distance describes the separation between individuals or social groups in society along dimensions such as social class, race/ethnicity, gender or sexuality.

Most of the notions of distance between two points or objects described above are examples of the mathematical idea of a metric. A metric or distance function is a function d which takes pairs of points or objects to real numbers and satisfies the following rules:
The distance between an object and itself is always zero. The distance between distinct objects is always positive. Distance is symmetric: the distance from x to y is always the same as the distance from y to x. Distance satisfies the triangle inequality: if x, y, and z are three objects, then This condition can be described informally as "intermediate stops can't speed you up." As an exception, many of the divergences used in statistics are not metrics.

The word distance is also used for related concepts that are not encompassed by the description "a numerical measurement of how far apart points or objects are".

The distance travelled by an object is the length of a specific path travelled between two points, such as the distance walked while navigating a maze. This can even be a closed distance along a closed curve which starts and ends at the same point, such as a ball thrown straight up, or the Earth when it completes one orbit. This is formalized mathematically as the arc length of the curve. The distance travelled may also be signed: a "forward" distance is positive and a "backward" distance is negative. Circular distance is the distance traveled by a point on the circumference of a wheel, which can be useful to consider when designing vehicles or mechanical gears (see also odometry). The circumference of the wheel is 2π × radius; if the radius is 1, each revolution of the wheel causes a vehicle to travel 2π radians.