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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. These names come from the ancient Greek mathematicians Euclid ...
Hausdorff distance. In mathematics, the Hausdorff distance, or Hausdorff metric, also called Pompeiu–Hausdorff distance, [1][2] measures how far two subsets of a metric space are from each other. It turns the set of non-empty compact subsets of a metric space into a metric space in its own right. It is named after Felix Hausdorff and Dimitrie ...
Distance from a point to a line. 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 ...
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 between the two points on the surface of the sphere. (By comparison, the shortest path passing through the sphere's interior is the chord between ...
In mathematics, the L p spaces are ... The Euclidean distance between two points and is the length ‖ ‖ of the straight line between the two points. In many ...
In mathematics, a metric space is a set together with a notion of distance between its elements, usually called points. The distance is measured by a function called a metric or distance function. [1] Metric spaces are the most general setting for studying many of the concepts of mathematical analysis and geometry.
On the number line, the distance between two points is the unit length if and only if the difference of the represented numbers equals 1. Other choices are possible. One of the most common choices is the logarithmic scale , which is a representation of the positive numbers on a line, such that the distance of two points is the unit length, if ...
In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector[ 1 ] or spatial vector[ 2 ]) is a geometric object that has magnitude (or length) and direction. Euclidean vectors can be added and scaled to form a vector space. A vector quantity is a vector-valued physical quantity, including ...