Distance

In the mathematical and physical sense the distance ( the distance, the distance ) between two points is the length of the straight line that connects the two.

The distance between two objects is the length of the shortest line connecting the two objects, that is, the length of the path which is delimited by the two mutually closest points of the two objects. Will not the other nearest points of two objects is considered, then this is stated explicitly or is derived from the context, such as the distance between the geometric centers or focal points.

The area of mathematics that deals with the distance measurement is the metric.

The distance, the distance, the distance between two values ​​of a quantity or between two points in time is determined by forming the absolute value of their difference, that is, by being subtracted from one another and is formed from the result of the absolute value. The measured distance is independent of the selected reference point of the coordinate system, but not of its scale (see scale).

In observational astronomy, the apparent distance between two celestial objects in the sky is as angular distance - the angle at which they appear - given.

The distance between two sets in Euclidean space ( or more generally, in a metric space ) can be defined by the Hausdorff metric.

Euclidean distance

In the Cartesian coordinate system to calculate the distance ( Euclidean distance ) between two points using the Pythagorean theorem:

The distance of a point on a straight line or a planar surface is the distance from the base point of the solder precipitated on it, which is always of a curved line a distance from one of its tangents.

Calculation options for the distances from points to straight lines or planes are listed in the formulary Analytic Geometry.

Distance measurement on curved surfaces

On the surface of the sphere is the distance along great circles is determined and specified in degrees or radians. To calculate the distance see orthodrome.

On the Erdellipsoid or other convex surfaces to use the geodesic line or the normal section.

In geodesy and geosciences one speaks rather of distance or distance that is specified metric.