Distance
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More Definitions for distance. See the full definition for distance in the English Language Learners Dictionary.
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Translation of distance for Spanish Speakers. Translation of distance for Arabic Speakers.
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The popular distance calculator calculates distances in kilometres between any locations and coordinates, providing route planners, interactive maps, and. Distance is a numerical measurement of how far apart objects are. In physics or everyday usage, distance may refer to a physical length or an estimation based.
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Synonyms for distance Synonyms: Noun lead , length , remove , spacing , spread , stretch , way Visit the Thesaurus for More. The gas station is a short distance away. Speed is measured in time and distance. She kept the children a safe distance from the road. The sign was hard to read from a distance.
We followed them at a distance. She feels a distance from her brother that wasn't there before. Although they were once good friends, there was now considerable distance between them.
Distance calculator
He wants to put distance between himself and his former boss. Distance cannot be negative , and never decreases. Distance is a scalar quantity, or a magnitude. Whereas displacement is a vector quantity with both magnitude and direction. It can be negative, zero, or positive. Directed distance does not measure movement, it measures the separation of two points, and can be a positive, zero, or negative vector.
The gas station is a short distance away. In most cases, "distance from A to B" is interchangeable with "distance from B to A". Astronomical system of units Cosmic distance ladder Distance geometry problem Dijkstra's algorithm Distance matrix Distance measuring equipment DME Distance-based road exit numbers Engineering tolerance Length Meridian arc Milestone Multiplicative distance Orders of magnitude length Proper length Proxemics — physical distance between people Rangefinder Signed distance function. As you start to write the name of a city or place, distance calculator will suggest you place names automatically, you may choose from them to calculate distance. You can help by adding to it. In graph theory the distance between two vertices is the length of the shortest path between those vertices.
The distance covered by a vehicle for example as recorded by an odometer , person, animal, or object along a curved path from a point A to a point B should be distinguished from the straight-line distance from A to B. For example, whatever the distance covered during a round trip from A to B and back to A , the displacement is zero as start and end points coincide. In general the straight-line distance does not equal distance travelled, except for journeys in a straight line.
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Directed distances along straight lines are vectors that give the distance and direction between a starting point and an ending point. Another kind of directed distance is that between two different particles or point masses at a given time. For instance, the distance from the center of gravity of the Earth A and the center of gravity of the Moon B which does not strictly imply motion from A to B falls into this category. A directed distance along a curved line is not a vector and is represented by a segment of that curved line defined by endpoints A and B , with some specific information indicating the sense or direction of an ideal or real motion from one endpoint of the segment to the other see figure.
For instance, just labelling the two endpoints as A and B can indicate the sense, if the ordered sequence A , B is assumed, which implies that A is the starting point. A displacement see above is a special kind of directed distance defined in mechanics. A directed distance is called displacement when it is the distance along a straight line minimum distance from A and B , and when A and B are positions occupied by the same particle at two different instants of time.
This implies motion of the particle. The distance traveled by a particle must always be greater than or equal to its displacement, with equality occurring only when the particle moves along a straight path. In analytic geometry , the distance between two points of the xy-plane can be found using the distance formula. The distance between x 1 , y 1 and x 2 , y 2 is given by:. Similarly, given points x 1 , y 1 , z 1 and x 2 , y 2 , z 2 in three-space , the distance between them is:. These formula are easily derived by constructing a right triangle with a leg on the hypotenuse of another with the other leg orthogonal to the plane that contains the 1st triangle and applying the Pythagorean theorem.
In the study of complicated geometries, we call this most common type of distance Euclidean distance , as it is derived from the Pythagorean theorem , which does not hold in non-Euclidean geometries. This distance formula can also be expanded into the arc-length formula.
In the Euclidean space R n , 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. 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 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.
The infinity norm distance is also called Chebyshev distance. In 2D, it is the minimum number of moves kings require to travel between two squares on a chessboard. The p -norm is rarely used for values of p other than 1, 2, and infinity, but see super ellipse. In physical space the Euclidean distance is in a way the most natural one, because in this case the length of a rigid body does not change with rotation.
The value of the integral D represents the length of this trajectory. In the familiar Euclidean case the above integral this optimal trajectory is simply a straight line. It is well known that the shortest path between two points is a straight line. Straight lines can formally be obtained by solving the Euler—Lagrange equations for the above functional. The Euclidean distance between two objects may also be generalized to the case where the objects are no longer points but are higher-dimensional manifolds , such as space curves, so in addition to talking about distance between two points one can discuss concepts of distance between two strings.
Since the new objects that are dealt with are extended objects not points anymore additional concepts such as non-extensibility, curvature constraints, and non-local interactions that enforce non-crossing become central to the notion of distance. The distance between the two manifolds is the scalar quantity that results from minimizing the generalized distance functional, which represents a transformation between the two manifolds:.
The above double integral is the generalized distance functional between two polymer conformation. If two discrete polymers are inextensible, then the minimal-distance transformation between them no longer involves purely straight-line motion, even on a Euclidean metric. There is a potential application of such generalized distance to the problem of protein folding [2] [3] This generalized distance is analogous to the Nambu—Goto action in string theory , however there is no exact correspondence because the Euclidean distance in 3-space is inequivalent to the spacetime distance minimized for the classical relativistic string.
This is a metric often used in computer vision that can be minimized by least squares estimation. It may serve as an "initial guess" for geometric distance to refine estimations of the curve by more accurate methods, such as non-linear least squares.