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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 from the point to the line is then just the norm of that vector. This more general formula is not restricted to two dimensions. Another vector formulation. If the vector space is orthonormal and if the line goes through point a and has a direction vector n, the distance between point p and the line is
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.
The great-circle distance, orthodromic distance, or spherical distance is the distance along a great circle . It is the shortest distance between two points on the surface of a sphere, measured along the surface of the sphere (as opposed to a straight line through the sphere's interior). The distance between two points in Euclidean space is the ...
The shortest distance along the surface of a sphere between two points on the surface is along the great-circle which contains the two points. The great-circle distance article gives the formula for calculating the shortest arch length D {\displaystyle D} on a sphere about the size of the Earth.
The distance formula in Cartesian coordinates is derived from the Pythagorean theorem. If (x 1, y 1) and (x 2, y 2) are points in the plane, then the distance between them, also called the Euclidean distance, is given by + ().
Vincenty's formulae. Vincenty's formulae are two related iterative methods used in geodesy to calculate the distance between two points on the surface of a spheroid, developed by Thaddeus Vincenty (1975a). They are based on the assumption that the figure of the Earth is an oblate spheroid, and hence are more accurate than methods that assume a ...
The distance between two parallel lines in the plane is the minimum distance between any two points. Formula and proof [ edit ] Because the lines are parallel, the perpendicular distance between them is a constant, so it does not matter which point is chosen to measure the distance.
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