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In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. A simple example is the circle. In everyday use of the term "curve", a straight line is not curved, but in mathematical parlance curves include straight lines and line segments. A large number of other curves have been studied in geometry.

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Wikipedia about curve

In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. A simple example is the circle. In everyday use of the term "curve", a straight line is not curved, but in mathematical parlance curves include straight lines and line segments. A large number of other curves have been studied in geometry.

This article is about the general theory. The term curve is also used in ways making it almost synonymous with mathematical function (as in learning curve), or graph of a function (Phillips curve).

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In mathematics, a (topological) curve is defined as follows: let I be an interval of real numbers (i.e. a non-empty connected subset of \mathbb{R}); then a curve \!\,\gamma is a continuous mapping \,\!\gamma : I \rightarrow X, where X is a topological space. The curve \!\,\gamma is said to be simple if it is injective, i.e. if for all x, y in I, we have \,\!\gamma(x) = \gamma(y) \implies x = y. If I is a closed bounded interval \,\!b, we also allow the possibility \,\!\gamma(a) = \gamma(b) (this convention makes it possible to talk about closed simple curve).

If \gamma(x)=\gamma(y) for some x\ne y (other than the extremities of I), then \gamma(x) is called a double (or multiple) point of the curve.

A curve \!\,\gamma is said to be closed or a loop if \,\!I = b and if \!\,\gamma(a) = \gamma(b). A closed curve is thus a continuous mapping of the circle S^1; a simple closed curve is also called a Jordan curve or a Jordan arc.

A plane curve is a curve for which X is the Euclidean plane  these are the examples first encountered  or in some cases the projective plane. A space curve is a curve for which X is of three dimensions, usually Euclidean space; a skew curve is a space curve which lies in no plane. These definitions also apply to algebraic curves (see below). However, in the case of algebraic curves it is very common not to restrict the curve to having points only defined over the real numbers.

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Curve

Official site of the U.K. rock band.www.curve.co.uk/

Curve Ball - Sports Game from AddictingGames

Curve Ball, a Sports Game from AddictingGames: Take pong to the third dimension and make the curve count. How many levels can you go through before running out of bluewww.addictinggames.com/curveball.html

The L-Curve: A Graph of the US Income Distribution

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News about Curve

Economy, learning curve hurting open-wheel drivers

Sports IllustratedKANSAS CITY, Kan. (AP) -- AJ Allmendinger won't be driving for Red Bull Racing next season, giving up his seat for the final seven races to look for a job.http://sportsillustrated.cnn.com/2008/racing/10/01/economy.a...

Amir Khan prepares to roll with the punches as part of learning curve

Times OnlineMany boxers have learnt their biggest lessons taking the blows as sparring partner to a great name.http://www.timesonline.co.uk/tol/sport/more_sport/article487...

Old Media Ahead Of Curve On Debate [New York Times]

GawkerWant to stay crucial moments ahead of your neighbors watching the vice presidential debate on a network feed? Try the Times' website . Not only is the old-media stalwart streaming live video of...http://gawker.com/5058421/old-media-ahead-of-curve-on-debate

Learning Curve Cannot Straighten Out The Chip Seal Mess

The ChattanooganWhy in heavens name is the city of Chattanooga going to resume the "chip seal" process this spring? Have they not seen the mess they have created? No matter what "learning curve" is involved, I cannot see how it will be any better in six months.http://www.chattanoogan.com/articles/article_136193.asp

Readers Write: Grass Valley has steep learning curve with bears

Sierra SunBears simply are not programmed to turn down a free and easy meal. Repeated offerings of sunflower seeds, garbage, and cracked corn are a guarantee for daily visits from the bruin that Grass Valley resident Ann Gilberg is now complaining about.http://www.sierrasun.com/article/20081001/OPINION/809309959/...

News about Curve

Rockdale County girl, 17, killed in car wreck

Atlanta Journal ConstitutionThe 17-year-old boy was driving south on Ebenezer when he lost control of the vehicle in a curve, Shupe said. He overcorrected and it rolled across the intersection at Potts and hit a tree, Shupe said. The driver and Crossley were trapped inside the ... http://www.ajc.com/metro/content/metro/stories/2008/10/12/ro...

Taameer has the head to reach heights

Daily TelegraphHe is still on a learning curve, but he is an exciting type who has been able to handle the razzmatazz [of raceday] much better than a lot of others. I’ll discuss his programme with the owner [Hamdan Al-Maktoum], but the 2,000 Guineas is ... http://www.telegraph.co.uk/sport/horseracing/3185015/Taameer...

Ozzie throws Gavin Floyd a curve with pitch supporting Mark Buehrle

New York Daily NewsCHICAGO - So much for confidence in your 17-game winner. After righthander Gavin Floyd spoke with the media prior to Game 3 Sunday about starting Monday if the White Sox staved off elimination, manager Ozzie Guillen said he would consider starting ... http://www.nydailynews.com/sports/baseball/2008/10/05/2008-1...

Big game on campus

Boston GlobeOn this balmy evening, no one is seeking cover. More than 20,000 people fill the respective Harvard and Holy Cross sides of the horseshoe, with the closed end of the field nearly empty except for kids running back and forth along the bottom curve of ... http://www.boston.com/travel/explorene/articles/2008/10/12/b...

C.Europe, Latam hit by credit crunch-Mexico's Ortiz

ForbesYou have to be perceived to be ahead of the curve. It is better to err on the side of doing too much than doing too little,' he said. (Reporting by Walter Brandimarte, Editing by Chizu Nomiyama) Keywords: FINANCIAL CRISIS/ORTIZ tf.TFN-Europe ... http://www.forbes.com/afxnewslimited/feeds/afx/2008/10/12/af...

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Industrial Design Magazine - Curve

Curve Industrial Design Magazine - subscribe online, advertise, id news, design, ideas, products, creative, innovationhttp://www.curve.com.au/

BlackBerry® Curve™ | The New Smartphone That's Brilliant and ...

BlackBerry Curve — the smallest, lightest BlackBerry smartphone with a full QWERTY keyboard. Packed with features: email, text and instant messaging, web browser, camera, maps ... http://www.blackberrycurve.com/

Altoona Curve

Official site of the Altoona, Pennsylvania Curve minor league baseball team.http://www.altoonacurve.com/

Curves Women's Only Health Clubs and Fitness Centers with Aerobic and ...

Curves is a women's gym that provides a total body workout with both aerobic and strength training that burns up to 500 calories in just 30 minutes. Curves is the largest fitness ... http://www.curves.com/

Curve Interactive

Are you making the most of online? Meet Curve - the dynamic new agency that's here to help. With strategic insights, creative energy and ... http://www.curve-interactive.com/
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Answers for Curve

manny3000

What is the reason for the steeper yield curve?

manny3000Anticipation of inflation requires a premium for longer holds.
Judah E

How to find formula of a curve when area underneath is known?

Judah EThis is really 2 questions. One is an exact answer. If you know the area under a curve for any value of x, then (if you know calculus) you can take the derivative of the area function to get the curve...
amyrhoo

What is the slowest speed at which that car can go around the curve?

amyrhooIf you consider a small enough part of the curve you get an inclined plane , with the centrifugal force pushing the car up the plane , and the mass pulling it down. The only difference between the lim...
eL Manchego

What is the derivation of the curve of the polar hyperbola?

eL ManchegoWhen you write the equation of a conic section in polar form, it is at its simplest when the focus is at the origin. This is a natural assumption when studying orbital mechanics. The equation of a...
A. M

How do I make the tips of my hair curve?

A. MThey usually have a special styling wax for that. You can get it at most hair salons. If you want really good results they usually work best with your hair in layers. If you often straighten it, and w...

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