|
This article is about distance in the mathematical / physical sense. For distance between people, see personal space, proxemics. Personal space is the region surrounding each person, which if violated makes them feel uncomfortable. ...
The term proxemics was introduced by anthropologist Edward T. Hall in 1963 to describe the measureable distances between people as they interacted. ...
The distance between two points is the length of a straight line between them. In the case of two locations on Earth, usually the distance along the surface is meant: either "as the crow flies" (along a great circle) or by road, railroad, etc. Distance is sometimes expressed in terms of the time to cover it, for example walking or by car. Sometimes a distance thus indicated is ambiguous because the means of transport is neither mentioned nor obvious. In general English usage, length (symbols: l, L) is but one particular instance of distance – an objects length is how long the object is – but in the physical sciences and engineering, the word length is in some contexts used synonymously with distance. Height is vertical distance; width (or breadth...
As the crow flies is a colloquial term used to describe the most direct route between two points on the Earth. ...
A road is a strip of land, smoothed or otherwise prepared to allow easier travel, connecting two or more destinations. ...
This is the top-level page of WikiProject trains Rail tracks Rail transport refers to the land transport of passengers and goods along railways or railroads. ...
Distance as mentioned above is sometimes not symmetric, hence not a metric (see below): this applies to distance by car in the case of one-way streets, and also in the case the distance is expressed in terms of the time to cover it (a road may be more crowded in one direction than in the other, for a ship upstream and downstream makes a difference). Italian barque Amerigo Vespucci in New York harbor, 1976. ...
As opposed to a position coordinate, a distance can not be negative. Distance is a scalar quantity, containing only a magnitude, whereas displacement is an equivalent vector quantity containing both magnitude and direction. Cartesian means relating to the French mathematician and philosopher Descartes, who, among other things, worked to merge algebra and Euclidean geometry. ...
A negative number is a number that is less than zero, such as −3. ...
The concept of a scalar is used in mathematics, physics, and computing. ...
Real numbers The magnitude of a real number is usually called the absolute value or modulus. ...
The term displacement can have one of several meanings, depending on context: Displacement (distance), a physical quantity in kinematics Particle displacement, acoustics of sound in air Displacement (fluid), a different physical quantity, used in fluid mechanics and navigation; used as a measure of a ships size Engine displacement, a...
In physics and engineering, the word vector typically refers to a quantity that has close relationship to the spatial coordinates, informally described as an object with a magnitude and a direction. The word vector is also now used for more general concepts (see also vector and generalizations below), but this...
The term direction can be applied to various topics. ...
Distance covered
 Distance along a path compared with displacement The distance covered by a vehicle (often recorded by a odometer), person, animal, object, etc. should be distinguished from the distance from starting point to end point, even if latter is taken to mean e.g. the shortest distance along the road, because a detour could be made, and the end point can even coincide with the starting point. distance v displacement File links The following pages link to this file: Distance Displacement (distance) Categories: GFDL images ...
distance v displacement File links The following pages link to this file: Distance Displacement (distance) Categories: GFDL images ...
An odometer comes from the Greek word hodós, meaning path or way and métron, measure. It is a device used for indicating distance traveled by an automobile or other vehicle. ...
Formal definition A distance between two points P and Q in a metric space is d(P,Q), where d is the distance function. We can also define the distance between two sets A and B in a metric space as being the minimum (or infimum) of distances between any two points P in A and Q in B. In mathematics, a metric space is a set where a notion of distance between elements of the set is defined. ...
In mathematics the infimum of a subset of some set is the greatest element, not necessarily in the subset, that is smaller than all other elements of the subset. ...
The distance formula The (Euclidean) distance, d, between two points expressed in Cartesian coordinates equals the square root of the sum of the squares of the changes of each coordinate. Thus, in a two-dimensional space The Euclidean distance of two points x = (x1,...,xn) and y = (y1,...,yn) in Euclidean n-space is computed as It is the ordinary distance between the two points that one would measure with a ruler, which can be proven by repeated application of the Pythagorean theorem. ...
Cartesian means relating to the French mathematician and philosopher Descartes, who, among other things, worked to merge algebra and Euclidean geometry. ...
In mathematics, the principal square root of a non-negative real number is denoted and represents the non-negative real number whose square (the result of multiplying the number by itself) is . ...
and in a three-dimensional space:
Here, "Δ" (delta) refers to the change in a variable. Thus, Δx is the change in x, pronounced as such, or as "delta-x". In mathematical terms, Δx = x1 − x0.
This distance formula can be seen as a specialized form of the Pythagorean theorem; it can also be expanded into the arc-length formula. In mathematics and in the sciences, a formula is a concise way of expressing information symbolically (as in a mathematical or chemical formula), or a general relationship between quantities. ...
There are thousands of proofs of the Pythagorean theorem. ...
Edge may have one of the following special meanings, in addition to its dictionary definition: wiktionary:edge. ...
Generalized distance in arbitrary dimensions: Norms In the Euclidean space Rn, the distance between two points is usually given by the Euclidean distance (2-norm distance). Other distances, based on other norms, are sometimes used instead. For a point (x1, x2, ...,xn) and a point (y1, y2, ...,yn), the distances are defined as: In mathematics and astronomy, Euclidean space is a generalization of the 2- and 3-dimensional spaces studied by Euclid. ...
In linear algebra, functional analysis and related areas of mathematics a norm is a function which assigns a positive length or size to all vectors in a vector space, other than the zero vector. ...
| 1-norm distance | | | 2-norm distance | | | p-norm distance | | | infinity norm distance | | | | The 2-norm distance is the Euclidean distance, a generalization of the Pythagorean theorem to more than two coordinates. It is what would be obtained if the distance between two points were measured with a ruler: the "intuitive" idea of distance. The Euclidean distance of two points x = (x1,...,xn) and y = (y1,...,yn) in Euclidean n-space is computed as It is the ordinary distance between the two points that one would measure with a ruler, which can be proven by repeated application of the Pythagorean theorem. ...
There are thousands of proofs of the Pythagorean theorem. ...
See Cartesian coordinate system or Coordinates (elementary mathematics) for a more elementary introduction to this topic. ...
The 1-norm distance is more colourfully called the taxicab norm or Manhattan distance, because it is the distance a car would drive in a city laid out in square blocks (if there are no one-way streets). Taxicab geometry, considered by Hermann Minkowski in the 19th century, is a form of geometry in which the usual metric of Euclidean geometry is replaced by a new metric in which the distance between two points is the sum of the (absolute) differences of their coordinates. ...
If you measure the strength of each of the n links in a chain (where larger numbers mean weaker links), then because a chain is only as strong as its weakest link, the strength of the chain will be the infinity-norm distance from the list of measurements to the origin.
The p-norm is rarely used for values of p other than 1, 2, and infinity, but see super ellipse. A superellipse is a geometrical figure which in a cartesian coordinate system can be described as the set of all points (x, y) with where and and are the radii of the oval shape. ...
Other norms Taxicab geometry, considered by Hermann Minkowski in the 19th century, is a form of geometry in which the usual metric of Euclidean geometry is replaced by a new metric in which the distance between two points is the sum of the (absolute) differences of their coordinates. ...
Taxicab geometry, considered by Hermann Minkowski in the 19th century, is a form of geometry in which the usual metric of Euclidean geometry is replaced by a new metric in which the distance between two points is the sum of the (absolute) differences of their coordinates. ...
In a plane, the Chebyshev distance between the point P1 with coordinates (x1, y1) and the point P2 at (x2, y2) is This concept is named after Pafnuty Chebyshev. ...
The king (♔♚) is a piece in the game of chess. ...
The queen is the most powerful piece in the game of chess. ...
A bishop moves only diagonally. ...
A chessboard is the board used in the game of chess, which consists of eight rows and eight columns of squares arranged in alternating colors. ...
Distances in other spaces Mahalanobis distance, in mathematics and statistics, is a distance measure invented by P. C. Mahalanobis in 1936. ...
Statistics is the science and practice of developing knowledge through the use of empirical data expressed in quantitative form. ...
In information theory, the Hamming distance is the number of positions in two strings of equal length for which the corresponding elements are different. ...
Coding theory deals with the properties of codes and thus with their fitness for a specific application. ...
In information theory, the Levenshtein distance or edit distance between two strings is given by the minimum number of operations needed to transform one string into the other, where an operation is an insertion, deletion, or substitution. ...
See also |
Feeds |
Contact