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Distance is a numerical description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical length, a period of time, or an estimation based on other criteria (e.g. "two counties over"). In mathematics, distance must meet more rigorous criteria.

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Wikipedia About Distance

Distance is a numerical description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical length, a period of time, or an estimation based on other criteria (e.g. "two counties over"). In mathematics, distance must meet more rigorous criteria.

In most cases there is symmetry and "distance from A to B" is interchangeable with "distance between B and A".

Geometry

In neutral geometry, the minimum distance between two points is the length of the line segment between them.

In analytic geometry, the distance between two points of the xy-plane can be found using the distance formula. The distance between (x1, y1) and (x2, y2) is given by

d=\sqrt{(\Delta x)^2+(\Delta y)^2}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.\,

Similarly, given points (x1, y1, z1) and (x2, y2, z2) in three-space, the distance between them is

d=\sqrt{(\Delta x)^2+(\Delta y)^2+(\Delta z)^2}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}.

Which is easily proven 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.

Distance in Euclidean space

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 Minkowski distance of order p (p-norm distance) is defined as: ^n \left| x_i - y_i \right| |- | 2-norm distance || = \left( \sum_{i=1}^n \left| x_i - y_i \right|^2 \right)^{1/2} |- | p-norm distance || = \left( \sum_{i=1}^n \left| x_i - y_i \right|^p \right)^{1/p} |- | infinity norm distance || = \lim_{p \to \infty} \left( \sum_{i=1}^n \left| x_i - y_i \right|^p \right)^{1/p} |- | || = \max \left(|x_1 - y_1|, |x_2 - y_2|, \ldots, |x_n - y_n| \right). |}

p need not be an integer, but it cannot be less than 1, because otherwise the triangle inequality does not hold.

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.

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News about Distance

Maine Senate debate long-distance affair

New England Cable News (NECN/WMTW) - Today, Maine Senator Susan Collins and Congressman Tom Allen met up for their second debate. This time, technology played a big part. The second of 10 planned Senate debates between Republican incumbent Susan Collins and Democrat Tom Allen turned out to be a long-distance affair, with Collins appearing by video conference. Fog canceled flights into Portland on Wednesday ...http://www.necn.com/Boston/Politics/Maine-Senate-debate-long...

Southlake Carroll Track Club claims distance medley relay title at Nike Outdoor Nationals

Southlake TimesBefore Colby Lowe took over the distance medley relay at the Nike Outdoor Nationals was somewhat in doubt.http://www.southlaketimes.com/articles/2008/10/02/southlake_...

Runner looking to distance himself from competition

The Colony Courier-LeaderThe Colony senior distance runner Alan Velazco came tantalizing close to his first state cross country berth last season. Eleven seconds to be exact.http://www.colonyleader.com/articles/2008/10/02/the_colony_c...

Haslett presides over Rams' fresh start

NFL.comOn his first full day as St. Louis Rams coach, Jim Haslett was impressed by the energy level in practice. What he experienced was a team eager to distance itself from a sorry 0-4 start.http://www.nfl.com/goto?id=09000d5d80b4e4fd

Spacing, Not Size, Matters In Visual Recognition, Researchers Find

Science DailyYou might think that the farthest distance at which you can hold a book and still read it quickly is determined by the size of the letters. However, neuroscientists have concluded that it's the spacing between letters, not their size, that matters. http://www.sciencedaily.com/releases/2008/09/080925144613.ht...

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A N Wilson: how Sartre came to be sidelined

Daily TelegraphHis defence of Communism - though late in the day he tried to distance himself from the worst excesses of the Soviet tyranny - was worse than ridiculous, it was morally abhorrent, and did much to blind the Western intelligentsia to the perils of ... http://www.telegraph.co.uk/arts/main.jhtml?xml=/arts/2008/10...

Motorway 'Lexus lanes' could be trialled within two years

Daily TelegraphThis would entail also installing time over distance speed cameras – already in used on some of Britain's roads - which would be able to tell whether drivers broke the limit. The plans were condemned by the AA. "Our members oppose them ... http://www.telegraph.co.uk/motoring/3184095/Motorway-Lexus-l...

Toby Flood demands share of attention

Times OnlineHook missed two from more than 40 metres, a distance ready-made for Gavin Henson, who was dropped for this game for disciplinary reasons. Sean Holley, their head coach, batted away questions about the Wales icon. “The case is closed,” he said ... http://www.timesonline.co.uk/tol/sport/rugby_union/article49...

Steel yourself: Richard Serra's monumental sculptures

The IndependentThen, after pacing steadfastly for what seems like a considerable distance, you come to an abrupt stop. The maze has suddenly turned back on itself, so you walk back in that same direction, except that this time the walls lean differently ... http://www.independent.co.uk/arts-entertainment/art-and-arch...

1968 Mexico City Olympic games heralded change

Miami HeraldOfficials had to unspool an old-fashioned measuring tape before they posted the distance of 8.90 meters. His record would last for 22 years. ''Ralph, how far is that?'' Beamon asked teammate Ralph Boston, gold medalist in 1960 and silver medalist in ... http://www.miamiherald.com/sports/story/722404.html

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Distance Learning

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Distance Learning - Spokane Community College

Distance learning courses offer students a flexible alternative to on-campus classes. The content, college credit, and transferability of distance learning courses are ... http://www.scc.spokane.edu/?dl

Distance -- from Wolfram MathWorld

The distance between two points is the length of the path connecting them. In the plane, the distance between points (x_1,y_1) and (x_2,y_2) is given by the Pythagorean theorem, d ... http://mathworld.wolfram.com/Distance.html
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Answers for Distance

X L M T DHow much distance will a vehicle having an acceleration of 0-60 km/h cover in 4 seconds?X L M T D60 km/hr is 16.7 m/s acceleration is 16.7 m/s / 4s = 4.17 m/s² d = ½at² =½4.17(4)² = 33.3 meters another method: if the acceleration is uniform, then the average speed is 8.33 m/s...euro4569Is Distance learning a more republican or democratic way of teaching. What political parties would prefer it?euro4569I would say that distant learing is definitely more of a democratic learning. This is because distant learning gives the option of education to a lot more people than education was available to in the...David SWhat is the maximum distance for the action of the strong nuclear force?David SThe strong nuclear force is not mediated by fermions - it is mediated by gluons, which are gauge vector bosons. Gluons mediate the strong attraction between quarks. Quarks make up the nucleons that...beebeepHow is distance calculated using the Nike ipod kit or with the Polar ds systems?beebeepMagic gnomes are in the chip and they count your steps. Honestly my mom told me.minimaxstatsWhat is the closest distance from pitcher to catcher at which you can throw a curveball?minimaxstats51
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