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The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be derived and expressed in several ways.
In Euclidean space, the distance from a point to a plane is the distance between a given point and its orthogonal projection on the plane, the perpendicular distance to the nearest point on the plane. It can be found starting with a change of variables that moves the origin to coincide with the given point then finding the point on the shifted ...
Euclidean distance. In mathematics, the Euclidean distance between two points in Euclidean space is the length of the line segment between them. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, and therefore is occasionally called the Pythagorean distance . These names come from the ancient Greek ...
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.
Geographical distance or geodetic distance is the distance measured along the surface of the Earth, or the shortest arch length. The formulae in this article calculate distances between points which are defined by geographical coordinates in terms of latitude and longitude .
History of the metre. An early definition of the metre was one ten-millionth of the Earth quadrant, the distance from the North Pole to the Equator, measured along a meridian through Paris. The history of the metre starts with the Scientific Revolution that is considered to have begun with Nicolaus Copernicus 's publication of De revolutionibus ...
The nanometre ( SI symbol: nm) is a unit of length in the metric system equal to 10−9 metres ( 1 1 000 000 000 m = 0.000 000 001 m ). To help compare different orders of magnitude, this section lists lengths between 10 −9 and 10 −8 m (1 nm and 10 nm). 1 nm – diameter of a carbon nanotube.
Distance between two metric-space subsets. In mathematics, the Hausdorff distance, or Hausdorff metric, also called Pompeiu–Hausdorff distance,[1][2]measures how far two subsetsof a metric spaceare from each other. It turns the set of non-emptycompactsubsets of a metric space into a metric space in its own right.