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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 .
Arc length is the distance between two points along a section of a curve. Development of a formulation of arc length suitable for applications to mathematics and the sciences is a focus of calculus .
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 spherical Earth, such ...
A diagram illustrating great-circle distance (drawn in red) between two points on a sphere, P and Q. Two antipodal points, u and v are also shown. The great-circle distance, orthodromic distance, or spherical distance is the distance between two points on a sphere, measured along the great-circle arc between them. This arc is the shortest path ...
The slant distance s (chord length) between two points can be reduced to the arc length on the ellipsoid surface S as: [21] = (+) / / where R is evaluated from Earth's azimuthal radius of curvature and h are ellipsoidal heights are each point. The first term on the right-hand side of the equation accounts for the mean elevation and the second ...
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.
For each type of object there are various similarity measurement formulas. [2] Similarity between two data points. Image shows the path of calculation when using the Euclidean distance formula. There are many various options available when it comes to finding similarity between two data points, some of which are a combination of other ...
The distance travelled by an object is the length of a specific path travelled between two points, [6] 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 .