Distance

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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. He wants to put distance between himself and his former boss.

Recent Examples on the Web: Noun If eyes are the window to your soul, then Jennifer Ejoke, known by her stage name Wavy the Creator, knows exactly how to keep the world at a mystifying distance with her permanent shades-up look. Verb Disney is gearing up to launch its own standalone streaming service in , and is in the process of distancing itself from Netflix.

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Distance Calculation Introduction

Was KFC's icon racist? First Known Use of distance Noun 14th century, in the meaning defined at sense 1 Verb , in the meaning defined at sense 1 Adjective , in the meaning defined above. History and Etymology for distance Noun see distant Verb see distant Adjective see distant. Learn More about distance. Resources for distance Time Traveler! Explore the year a word first appeared. Dictionary Entries near distance distal distal convoluted tubule distale distance distance flag distance language distance learning.

Time Traveler for distance The first known use of distance was in the 14th century See more words from the same century. Kids Definition of distance. More from Merriam-Webster on distance Thesaurus: All synonyms and antonyms for distance Spanish Central: Translation of distance Nglish: Translation of distance for Spanish Speakers Britannica English: Comments on distance What made you want to look up distance?

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Get Word of the Day daily email! 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.

Distance | Definition of Distance by Merriam-Webster

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. In mathematics , in particular geometry , a distance function on a given set M is a function d: For example, the usual definition of distance between two real numbers x and y is: This definition satisfies the three conditions above, and corresponds to the standard topology of the real line.

Distance calculator

But distance on a given set is a definitional choice. Another possible choice is to define: This also defines a metric, but gives a completely different topology, the " discrete topology "; with this definition numbers cannot be arbitrarily close. Various distance definitions are possible between objects. For example, between celestial bodies one should not confuse the surface-to-surface distance and the center-to-center distance. If the former is much less than the latter, as for a low earth orbit , the first tends to be quoted altitude , otherwise, e.

There are two common definitions for the distance between two non-empty subsets of a given metric space:. The distance between a point and a set is the infimum of the distances between the point and those in the set.