Search results
Results from the WOW.Com Content Network
Taxicab geometry or Manhattan geometry is geometry where the familiar Euclidean distance is ignored, and the distance between two points is instead defined to be the sum of the absolute differences of their respective Cartesian coordinates, a distance function (or metric) called the taxicab distance, Manhattan distance, or city block distance.
Other common distances in real coordinate spaces and function spaces: [27] Chebyshev distance (L ∞ distance), which measures distance as the maximum of the distances in each coordinate. Taxicab distance (L 1 distance), also called Manhattan distance, which measures distance as the sum of the distances in each coordinate.
In the Euclidean TSP (see below), the distance between two cities is the Euclidean distance between the corresponding points. In the rectilinear TSP, the distance between two cities is the sum of the absolute values of the differences of their x- and y-coordinates. This metric is often called the Manhattan distance or city-block metric.
Manhattan distance is commonly used in GPS applications, as it can be used to find the shortest route between two addresses. [ citation needed ] When you generalize the Euclidean distance formula and Manhattan distance formula you are left with the Minkowski distance formulas, which can be used in a wide variety of applications.
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.
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
The Minkowski distance or Minkowski metric is a metric in a normed vector space which can be considered as a generalization of both the Euclidean distance and the Manhattan distance. It is named after the Polish mathematician Hermann Minkowski .
The name relates to the distance a taxi has to drive in a rectangular street grid (like that of the New York borough of Manhattan) to get from the origin to the point . The set of vectors whose 1-norm is a given constant forms the surface of a cross polytope , which has dimension equal to the dimension of the vector space minus 1.