![Distance board in Vizag](https://upload.wikimedia.org/wikipedia/commons/6/6c/Distance_board_in_Vizag.jpg)
Distance is a numerical or occasionally qualitative
measurement of how far apart objects or points are. In
physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
or everyday usage, distance may refer to a physical
length or an estimation based on other criteria (e.g. "two counties over"). Since
spatial cognition is a rich source of
conceptual metaphor
In cognitive linguistics, conceptual metaphor, or cognitive metaphor, refers to the understanding of one idea, or conceptual domain, in terms of another. An example of this is the understanding of quantity in terms of directionality (e.g. "the pr ...
s in
human thought, the term is also frequently used metaphorically to mean a measurement of the amount of difference between two similar objects (such as
statistical distance between
probability distributions or
edit distance
In computational linguistics and computer science, edit distance is a string metric, i.e. a way of quantifying how dissimilar two strings (e.g., words) are to one another, that is measured by counting the minimum number of operations required to ...
between
strings of text) or a degree of separation (as exemplified by
distance
Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two counties over"). ...
between people in a
social network
A social network is a social structure made up of a set of social actors (such as individuals or organizations), sets of dyadic ties, and other social interactions between actors. The social network perspective provides a set of methods for ...
). Most such notions of distance, both physical and metaphorical, are formalized in
mathematics using the notion of a
metric space
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. Metric spaces are the most general set ...
.
In the
social science
Social science is one of the branches of science, devoted to the study of societies and the relationships among individuals within those societies. The term was formerly used to refer to the field of sociology, the original "science of so ...
s, distance can refer to a qualitative measurement of separation, such as
social distance
In sociology, social distance describes the distance between individuals or social groups in society, including dimensions such as social class, race/ethnicity, gender or sexuality. Members of different groups mix less than members of the same g ...
or
psychological distance Psychological distance is the degree to which people feel removed from a phenomenon. Distance in this case is not limited to the physical surroundings, rather it could also be abstract. Distance can be defined as the separation between the self and ...
.
Distances in physics and geometry
The distance between physical locations can be defined in different ways in different contexts.
Straight-line or Euclidean distance
The distance between two points in physical
space
Space is the boundless three-dimensional extent in which objects and events have relative position and direction. In classical physics, physical space is often conceived in three linear dimensions, although modern physicists usually cons ...
is the
length of a
straight line
In geometry, a line is an infinitely long object with no width, depth, or curvature. Thus, lines are one-dimensional objects, though they may exist in two, three, or higher dimension spaces. The word ''line'' may also refer to a line segmen ...
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 mathematics, the Euclidean distance between two points in Euclidean space is the length of a line segment between the two points.
It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, therefor ...
in
two- and
three-dimensional space
Three-dimensional space (also: 3D space, 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called ''parameters'') are required to determine the position of an element (i.e., point). This is the informa ...
. In
Euclidean geometry
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry: the '' Elements''. Euclid's approach consists in assuming a small set of intuitively appealing axioms ...
, the distance between two points and is often denoted
. In
coordinate geometry
In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry.
Analytic geometry is used in physics and engineerin ...
, Euclidean distance is computed using the
Pythagorean theorem. The distance between points and in the plane is given by:
Similarly, given points (''x''
1, ''y''
1, ''z''
1) and (''x''
2, ''y''
2, ''z''
2) in three-dimensional space, the distance between them is:
This idea generalizes to higher-dimensional
Euclidean space
Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, that is, in Euclid's ''Elements'', it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidean ...
s.
Measurement
There are many ways of
measuring
Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events.
In other words, measurement is a process of determining how large or small a physical quantity is as compared ...
straight-line distances. For example, it can be done directly using a
ruler
A ruler, sometimes called a rule, line gauge, or scale, is a device used in geometry and technical drawing, as well as the engineering and construction industries, to measure distances or draw straight lines.
Variants
Rulers have long ...
, or indirectly with a
radar
Radar is a detection system that uses radio waves to determine the distance ('' ranging''), angle, and radial velocity of objects relative to the site. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, we ...
(for long distances) or
interferometry (for very short distances). The
cosmic distance ladder
The cosmic distance ladder (also known as the extragalactic distance scale) is the succession of methods by which astronomers determine the distances to celestial objects. A ''direct'' distance measurement of an astronomical object is possible o ...
is a set of ways of measuring extremely long distances.
Shortest-path distance on a curved surface
![Greatcircle Jetstream routes](https://upload.wikimedia.org/wikipedia/commons/7/79/Greatcircle_Jetstream_routes.svg)
The straight-line distance between two points on the surface of the Earth is not very useful for most purposes, since we cannot tunnel straight through the
Earth's mantle
Earth's mantle is a layer of silicate rock between the crust and the outer core. It has a mass of 4.01 × 1024 kg and thus makes up 67% of the mass of Earth. It has a thickness of making up about 84% of Earth's volume. It is predominantly so ...
. Instead, one typically measures the shortest path along the
surface of the Earth,
as the crow flies
__NOTOC__
The expression ''as the crow flies'' is an idiom for the most direct path between two points, rather similar to "in a beeline". This meaning is attested from the early 19th century, and appeared in Charles Dickens's 1838 novel ''Oliver ...
. This is approximated mathematically by the
great-circle distance on a sphere.
More generally, the shortest path between two points along a
curved surface is known as a
geodesic. The
arc length
ARC may refer to:
Business
* Aircraft Radio Corporation, a major avionics manufacturer from the 1920s to the '50s
* Airlines Reporting Corporation, an airline-owned company that provides ticket distribution, reporting, and settlement services
* ...
of geodesics gives a way of measuring distance from the perspective of an
ant
Ants are eusocial insects of the family Formicidae and, along with the related wasps and bees, belong to the order Hymenoptera. Ants evolved from vespoid wasp ancestors in the Cretaceous period. More than 13,800 of an estimated total of ...
or other flightless creature living on that surface.
Effects of relativity
In the
theory of relativity
The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in ...
, because of phenomena such as
length contraction
Length contraction is the phenomenon that a moving object's length is measured to be shorter than its proper length, which is the length as measured in the object's own rest frame. It is also known as Lorentz contraction or Lorentz–FitzGerald ...
and the
relativity of simultaneity, distances between objects depend on a choice of
inertial frame of reference
In classical physics and special relativity, an inertial frame of reference (also called inertial reference frame, inertial frame, inertial space, or Galilean reference frame) is a frame of reference that is not undergoing any acceleration. ...
. On galactic and larger scales, the measurement of distance is also affected by the
expansion of the universe. In practice, a number of
distance measure
Distance measures are used in physical cosmology to give a natural notion of the distance between two objects or events in the universe. They are often used to tie some ''observable'' quantity (such as the luminosity of a distant quasar, the red ...
s are used in
cosmology
Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe. The term ''cosmology'' was first used in English in 1656 in Thomas Blount's ''Glossographia'', and in 1731 taken up in Latin by German philosopher ...
to quantify such distances.
Other spatial distances
![Manhattan distance](https://upload.wikimedia.org/wikipedia/commons/0/08/Manhattan_distance.svg)
Unusual definitions of distance can be helpful to model certain physical situations, but are also used in theoretical mathematics:
* In practice, one is often interested in the travel distance between two points along roads, rather than as the crow flies. In a
grid plan, the travel distance between street corners is given by the
Manhattan distance
A taxicab geometry or a Manhattan geometry is a geometry whose usual distance function or 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 Cartesian co ...
: the number of east–west and north–south blocks one must traverse to get between those two points.
* Chessboard distance, formalized as
Chebyshev distance
In mathematics, Chebyshev distance (or Tchebychev distance), maximum metric, or L∞ metric is a metric defined on a vector space where the distance between two vectors is the greatest of their differences along any coordinate dimension. It is n ...
, is the minimum number of moves a
king
King is the title given to a male monarch in a variety of contexts. The female equivalent is queen, which title is also given to the consort of a king.
*In the context of prehistory, antiquity and contemporary indigenous peoples, the tit ...
must make on a
chessboard in order to travel between two squares.
Metaphorical distances
Many abstract notions of distance used in mathematics, science and engineering represent a degree of difference or separation between similar objects. This page gives a few examples.
Statistical distances
In
statistics and
information geometry
Information geometry is an interdisciplinary field that applies the techniques of differential geometry to study probability theory and statistics. It studies statistical manifolds, which are Riemannian manifolds whose points correspond to pro ...
,
statistical distances measure the degree of difference between two
probability distributions. There are many kinds of statistical distances, typically formalized as
divergences; these allow a set of probability distributions to be understood as a
geometrical object called a
statistical manifold
In mathematics, a statistical manifold is a Riemannian manifold, each of whose points is a probability distribution. Statistical manifolds provide a setting for the field of information geometry. The Fisher information metric provides a met ...
. The most elementary is the
squared Euclidean distance
In mathematics, the Euclidean distance between two points in Euclidean space is the length of a line segment between the two Point (geometry), points.
It can be calculated from the Cartesian coordinates of the points using the Pythagorean theo ...
, which is minimized by the
least squares method; this is the most basic
Bregman divergence
In mathematics, specifically statistics and information geometry, a Bregman divergence or Bregman distance is a measure of difference between two points, defined in terms of a strictly convex function; they form an important class of divergences. W ...
. The most important in
information theory is the
relative entropy
Relative may refer to:
General use
*Kinship and family, the principle binding the most basic social units society. If two people are connected by circumstances of birth, they are said to be ''relatives''
Philosophy
*Relativism, the concept that ...
(
Kullback–Leibler divergence
In mathematical statistics, the Kullback–Leibler divergence (also called relative entropy and I-divergence), denoted D_\text(P \parallel Q), is a type of statistical distance: a measure of how one probability distribution ''P'' is different fr ...
), which allows one to analogously study
maximum likelihood estimation
In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed stati ...
geometrically; this is an example of both an
''f''-divergence and a Bregman divergence (and in fact the only example which is both). Statistical manifolds corresponding to Bregman divergences are
flat manifold In mathematics, a Riemannian manifold is said to be flat if its Riemann curvature tensor is everywhere zero. Intuitively, a flat manifold is one that "locally looks like" Euclidean space in terms of distances and angles, e.g. the interior angles o ...
s in the corresponding geometry, allowing an analog of the
Pythagorean theorem (which holds for squared Euclidean distance) to be used for
linear inverse problem
An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in X-ray computed tomography, source reconstruction in acoustics, or calculating the ...
s in inference by
optimization theory
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...
.
Other important statistical distances include the
Mahalanobis distance and the
energy distance.
Edit distances
In
computer science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (includi ...
, an
edit distance
In computational linguistics and computer science, edit distance is a string metric, i.e. a way of quantifying how dissimilar two strings (e.g., words) are to one another, that is measured by counting the minimum number of operations required to ...
or
string metric
In mathematics and computer science, a string metric (also known as a string similarity metric or string distance function) is a metric that measures distance ("inverse similarity") between two text strings for approximate string matching or comp ...
between two
strings measures how different they are. For example, the words "dog" and "dot", which differ by just one letter, are closer than "dog" and "cat", which have no letters in common. This idea is used in
spell checkers and in
coding theory
Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography, error detection and correction, data transmission and data storage. Codes are studied ...
, and is mathematically formalized in a number of different ways, including
Levenshtein distance
In information theory, linguistics, and computer science, the Levenshtein distance is a string metric for measuring the difference between two sequences. Informally, the Levenshtein distance between two words is the minimum number of single-charac ...
,
Hamming distance
In information theory, the Hamming distance between two strings of equal length is the number of positions at which the corresponding symbols are different. In other words, it measures the minimum number of ''substitutions'' required to chan ...
,
Lee distance In coding theory, the Lee distance is a distance between two strings x_1 x_2 \dots x_n and y_1 y_2 \dots y_n of equal length ''n'' over the ''q''-ary alphabet of size . It is a metric defined as
\sum_^n \min(, x_i - y_i, ,\, q - , x_i - y_i, ).
I ...
, and
Jaro–Winkler distance
In computer science and statistics, the Jaro–Winkler distance is a string metric measuring an edit distance between two sequences. It is a variant proposed in 1990 by William E. Winkler of the Jaro distance metric (1989, Matthew A. Jaro).
...
.
Distance in graph theory
In a
graph
Graph may refer to:
Mathematics
*Graph (discrete mathematics), a structure made of vertices and edges
**Graph theory, the study of such graphs and their properties
*Graph (topology), a topological space resembling a graph in the sense of discre ...
, the
distance
Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two counties over"). ...
between two vertices is measured by the length of the shortest
edge path between them. For example, if the graph represents a
social network
A social network is a social structure made up of a set of social actors (such as individuals or organizations), sets of dyadic ties, and other social interactions between actors. The social network perspective provides a set of methods for ...
, then the idea of
six degrees of separation
Six degrees of separation is the idea that all people are six or fewer social connections away from each other. As a result, a chain of "friend of a friend" statements can be made to connect any two people in a maximum of six steps. It is also k ...
can be interpreted mathematically as saying that the distance between any two vertices is at most six. Similarly, the
Erdős number
The Erdős number () describes the "collaborative distance" between mathematician Paul Erdős and another person, as measured by authorship of mathematical papers. The same principle has been applied in other fields where a particular individual ...
and the
Bacon number
Six Degrees of Kevin Bacon or Bacon's Law is a parlor game where players challenge each other to arbitrarily choose an actor and then connect them to another actor via a film that both actors have appeared in together, repeating this process to t ...
—the number of collaborative relationships away a person is from prolific mathematician
Paul Erdős and actor
Kevin Bacon
Kevin Norwood Bacon (born July 8, 1958) is an American actor. His films include the musical-drama film '' Footloose'' (1984), the controversial historical conspiracy legal thriller '' JFK'' (1991), the legal drama '' A Few Good Men'' (1992), t ...
, respectively—are distances in the graphs whose edges represent mathematical or artistic collaborations.
In the social sciences
In
psychology
Psychology is the scientific study of mind and behavior. Psychology includes the study of conscious and unconscious phenomena, including feelings and thoughts. It is an academic discipline of immense scope, crossing the boundaries between ...
,
human geography
Human geography or anthropogeography is the branch of geography that studies spatial relationships between human communities, cultures, economies, and their interactions with the environment. It analyzes spatial interdependencies between social i ...
, and the
social science
Social science is one of the branches of science, devoted to the study of societies and the relationships among individuals within those societies. The term was formerly used to refer to the field of sociology, the original "science of so ...
s, distance is often theorized not as an objective numerical measurement, but as a qualitative description of a subjective experience. For example,
psychological distance Psychological distance is the degree to which people feel removed from a phenomenon. Distance in this case is not limited to the physical surroundings, rather it could also be abstract. Distance can be defined as the separation between the self and ...
is "the different ways in which an object might be removed from" the self along dimensions such as "time, space, social distance, and hypotheticality".
In
sociology
Sociology is a social science that focuses on society, human social behavior, patterns of social relationships, social interaction, and aspects of culture associated with everyday life. It uses various methods of empirical investigation an ...
,
social distance
In sociology, social distance describes the distance between individuals or social groups in society, including dimensions such as social class, race/ethnicity, gender or sexuality. Members of different groups mix less than members of the same g ...
describes the separation between individuals or
social groups
In the social sciences, a social group can be defined as two or more people who interact with one another, share similar characteristics, and collectively have a sense of unity. Regardless, social groups come in a myriad of sizes and varieties ...
in
society
A society is a group of individuals involved in persistent social interaction, or a large social group sharing the same spatial or social territory, typically subject to the same political authority and dominant cultural expectations. Soci ...
along dimensions such as
social class,
race
Race, RACE or "The Race" may refer to:
* Race (biology), an informal taxonomic classification within a species, generally within a sub-species
* Race (human categorization), classification of humans into groups based on physical traits, and/or s ...
/
ethnicity,
gender
Gender is the range of characteristics pertaining to femininity and masculinity and differentiating between them. Depending on the context, this may include sex-based social structures (i.e. gender roles) and gender identity. Most cultures ...
or
sexuality.
Mathematical formalization
Most of the notions of distance between two points or objects described above are examples of the mathematical idea of a
metric
Metric or metrical may refer to:
* Metric system, an internationally adopted decimal system of measurement
* An adjective indicating relation to measurement in general, or a noun describing a specific type of measurement
Mathematics
In mathem ...
. A ''metric'' or ''distance function'' is a
function
Function or functionality may refer to:
Computing
* Function key, a type of key on computer keyboards
* Function model, a structured representation of processes in a system
* Function object or functor or functionoid, a concept of object-oriente ...
which takes pairs of points or objects to
real numbers and satisfies the following rules:
# The distance between an object and itself is always zero.
# The distance between distinct objects is always positive.
# Distance is
symmetric
Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definiti ...
: the distance from to is always the same as the distance from to .
# Distance satisfies the
triangle inequality
In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.
This statement permits the inclusion of degenerate triangles, but ...
: if , , and are three objects, then
This condition can be described informally as "intermediate stops can't speed you up."
As an exception, many of the
divergence
In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the quantity of the vector field's source at each point. More technically, the divergence represents the volume density of t ...
s used in statistics are not metrics.
Distance between sets
![Distance between sets](https://upload.wikimedia.org/wikipedia/commons/9/97/Distance_between_sets.svg)
There are multiple ways of measuring the physical distance between objects that
consist of more than one point:
* One may measure the distance between representative points such as the
center of mass; this is used for astronomical distances such as the
Earth–Moon distance.
* One may measure the distance between the closest points of the two objects; in this sense, the
altitude
Altitude or height (also sometimes known as depth) is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The exact definition and reference datum varies according to the context ...
of an airplane or spacecraft is its distance from the Earth. The same sense of distance is used in Euclidean geometry to define
distance from a point to a line In Euclidean geometry, the distance from a point to a line'' is the shortest distance from a given point to any point on an infinite straight line. It is the perpendicular distance of the point to the line, the length of the line segment which join ...
,
distance from a point to a plane In Euclidean space, the distance from a point to a plane is the distance between a given point and its orthogonal projection on the plane, the perpendicular distance to the nearest point on the plane.
It can be found starting with a change of varia ...
, or, more generally,
perpendicular distance between
affine subspace
In mathematics, an affine space is a geometric structure that generalizes some of the properties of Euclidean spaces in such a way that these are independent of the concepts of distance and measure of angles, keeping only the properties related ...
s.
: Even more generally, this idea can be used to define the distance between two
subsets of a metric space. The distance between sets and is the
infimum
In mathematics, the infimum (abbreviated inf; plural infima) of a subset S of a partially ordered set P is a greatest element in P that is less than or equal to each element of S, if such an element exists. Consequently, the term ''greatest lo ...
of the distances between any two of their respective points:
This does not define a metric on the set of such subsets: the distance between overlapping sets is zero, and this distance does not satisfy the triangle inequality for any metric space with two or more points (consider the triple of sets consisting of two distinct singletons and their union).
* The
Hausdorff distance In mathematics, the Hausdorff distance, or Hausdorff metric, also called Pompeiu–Hausdorff distance, 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 me ...
between two subsets of a metric space can be thought of as measuring how far they are from perfectly overlapping. Somewhat more precisely, the Hausdorff distance between and is either the distance from to the farthest point of , or the distance from to the farthest point of , whichever is larger. (Here "farthest point" must be interpreted as a supremum.) The Hausdorff distance defines a metric on the set of
compact subsets of a metric space.
Related ideas
The word distance is also used for related concepts that are not encompassed by the description "a numerical measurement of how far apart points or objects are".
Distance travelled
The distance travelled by an object is the length of a specific path travelled between two points,
such as the distance walked while navigating a
maze. This can even be a closed distance along a
closed curve
In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight.
Intuitively, a curve may be thought of as the trace left by a moving point. This is the definition that ...
which starts and ends at the same point, such as a ball thrown straight up, or the Earth when it completes one
orbit
In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as ...
. This is formalized mathematically as the
arc length
ARC may refer to:
Business
* Aircraft Radio Corporation, a major avionics manufacturer from the 1920s to the '50s
* Airlines Reporting Corporation, an airline-owned company that provides ticket distribution, reporting, and settlement services
* ...
of the curve.
The distance travelled may also be
signed: a "forward" distance is positive and a "backward" distance is negative.
Circular distance is the distance traveled by a point on the circumference of a
wheel, which can be useful to consider when designing vehicles or mechanical gears (see also
odometry
Odometry is the use of data from motion sensors to estimate change in position over time. It is used in robotics by some legged or wheeled robots to estimate their position relative to a starting location. This method is sensitive to errors due t ...
). The circumference of the wheel is ; if the radius is 1, each revolution of the wheel causes a vehicle to travel radians.
Displacement and directed distance
![Distancedisplacement](https://upload.wikimedia.org/wikipedia/commons/4/40/Distancedisplacement.svg)
The
displacement
Displacement may refer to:
Physical sciences
Mathematics and Physics
* Displacement (geometry), is the difference between the final and initial position of a point trajectory (for instance, the center of mass of a moving object). The actual path ...
in classical physics measures the change in position of an object during an interval of time. While distance is a
scalar quantity, or a
magnitude
Magnitude may refer to:
Mathematics
*Euclidean vector, a quantity defined by both its magnitude and its direction
*Magnitude (mathematics), the relative size of an object
*Norm (mathematics), a term for the size or length of a vector
*Order of ...
, displacement is a
vector
Vector most often refers to:
*Euclidean vector, a quantity with a magnitude and a direction
*Vector (epidemiology), an agent that carries and transmits an infectious pathogen into another living organism
Vector may also refer to:
Mathematic ...
quantity with both magnitude and
direction. In general, the vector measuring the difference between two locations (the
relative position) is sometimes called the directed distance.
For example, the directed distance from the
New York City Main Library flag pole to the
Statue of Liberty flag pole has:
* A starting point: library flag pole
* An ending point: statue flag pole
* A direction: -38°
* A distance: 8.72 km
Signed distance
See also
*
Absolute difference
The absolute difference of two real numbers x and y is given by , x-y, , the absolute value of their difference. It describes the distance on the real line between the points corresponding to x and y. It is a special case of the Lp distance for ...
*
Astronomical system of units
The astronomical system of units, formerly called the IAU (1976) System of Astronomical Constants, is a system of measurement developed for use in astronomy. It was adopted by the International Astronomical Union (IAU) in 1976 via Resolution No. ...
*
Color difference
*
Closeness (mathematics)
*
Distance geometry problem
*
Dijkstra's algorithm
Dijkstra's algorithm ( ) is an algorithm for finding the shortest paths between nodes in a graph, which may represent, for example, road networks. It was conceived by computer scientist Edsger W. Dijkstra in 1956 and published three years ...
*
Distance matrix
In mathematics, computer science and especially graph theory, a distance matrix is a square matrix (two-dimensional array) containing the distances, taken pairwise, between the elements of a set. Depending upon the application involved, the ''dist ...
*
Distance set
In geometry, the distance set of a collection of points is the set of distances between distinct pairs of points. Thus, it can be seen as the generalization of a difference set, the set of distances (and their negations) in collections of number ...
*
Engineering tolerance
Engineering tolerance is the permissible limit or limits of variation in:
# a physical dimension;
# a measured value or physical property of a material, manufactured object, system, or service;
# other measured values (such as temperature, hum ...
*
Multiplicative distance In algebraic geometry, \mu is said to be a multiplicative distance function over a field if it satisfies.
* \mu(AB)>1.\,
* ''AB'' is congruent to A'B' iff \mu(AB)=\mu(A'B').\,
* ''AB'' < ''A'B''' iff
*
Optical path length
*
Orders of magnitude (length)
The following are examples of orders of magnitude for different lengths.
__TOC__
Overview
Detailed list
To help compare different orders of magnitude, the following list describes various lengths between 1.6 \times 10^ metres and 10 ...
*
Proper length
Proper length or rest length is the length of an object in the object's rest frame.
The measurement of lengths is more complicated in the theory of relativity than in classical mechanics. In classical mechanics, lengths are measured based on ...
*
Proxemics
Proxemics is the study of human use of space and the effects that population density has on behaviour, communication, and social interaction.
Proxemics is one among several subcategories in the study of nonverbal communication, including haptics ...
– physical distance between people
*
Signed distance function
In mathematics and its applications, the signed distance function (or oriented distance function) is the orthogonal distance of a given point ''x'' to the boundary of a set Ω in a metric space, with the sign determined by whether or not ''x' ...
*
Similarity measure
In statistics and related fields, a similarity measure or similarity function or similarity metric is a real-valued function that quantifies the similarity between two objects. Although no single definition of a similarity exists, usually such meas ...
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Social distancing
In public health, social distancing, also called physical distancing, (NB. Regula Venske is president of the PEN Centre Germany.) is a set of non-pharmaceutical interventions or measures intended to prevent the spread of a contagious dis ...
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Vertical distance
Vertical position or vertical location, also known as vertical level or simply level, is a position along a vertical direction above or below a given vertical datum (reference level).
Vertical distance or vertical separation is the distance betwe ...
Library support
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Python (programming language)
Python is a high-level, general-purpose programming language. Its design philosophy emphasizes code readability with the use of significant indentation.
Python is dynamically-typed and garbage-collected. It supports multiple programming p ...
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Interspace-A package for finding the distance between two vectors, numbers and strings.
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-Distance computations (
scipy.spatial.distance
)
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Julia (programming language)
Julia is a high-level, dynamic programming language. Its features are well suited for numerical analysis and computational science.
Distinctive aspects of Julia's design include a type system with parametric polymorphism in a dynamic program ...
Julia Statistics Distance-A Julia package for evaluating distances (metrics) between vectors.
References
Bibliography
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