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[[File:Winding Number Around Point.svg|thumb|300px|This curve has total curvature 6''π'', and index/turning number 3, though it only has [[winding number]] 2 about ''p''.]]
They really do not appreciate the pastime, and they don't realize the magnitude or impact soccer has on the human race. There is no need to worry, If one does not have all the above characteristics, think success is not a heavenly fruit, as if one can only dream of it, everybody can achieve it with various techniques. You must watch the goal of season when he equals the highest number of goals in Spain. Also, he won the European cup thrice with Ajax and was voted European team player in 1999. The players wish to build a strong team of footballers who can easily snatch success from competitors. <br><br>2005 marked the milestone in [http://search.un.org/search?ie=utf8&site=un_org&output=xml_no_dtd&client=UN_Website_en&num=10&lr=lang_en&proxystylesheet=UN_Website_en&oe=utf8&q=Ronaldinho%27s+career&Submit=Go Ronaldinho's career] when he won the two prizes: European Footballer of the Year and FIFA World Player of the Year. The Forlan fan site started for him provides all the information's and the biography of him with his full history which can be viewed by any of his fan at any time. Later these teams went on to win round of 16 stage also and entered quarter finals. For goal scoring opportunities, the lobbed pass is the best option, and a lobbed ball is hard to block or intercept. For soccer fans watching this match on television, English broadcast will be provided by big ESPN (Direc - TV channel) at 2:30 p. <br><br>FIFA Soccer 11 is the latest soccer game developed by EA Sports. And last store them to a safe partition on computer. Those who are actually selling or farming coins will be banned from all EA games forever. In addition, Adidas also provided the game ball for the European Cup, Champions League and other games. However may fans of Donovan think it was a personal shot at the star. <br><br>The American foreigner &#305;s trained to an ally for soccer, and not a promoter. After retirement, Maradona spent most of his time in Cuba (can say in hospital), and after returning to Argentina suddently he suffered a major heart attack following a cocaine overdose and was admitted to intensive care in a Buenos Aires hospital. Xavi (Midfielder, Spain): If anyone would have watched you wins most season, his four awesome goals against archrivals Real Madrid in 2009, leading to the Barcelona club victory by 6-2, he would have enjoyed the contest thoroughly. We'll see if they can keep the momentum against Gabon next month. Iconic number 7's are David Villa, Raul Gonzalez, Franck Ribery, Luis Figo, George Best, Eric Cantona, Juanito, Amaro, David Beckham, Cristiano Ronaldo, Bastian Schweinsteiger and Andriy Schevchenko. <br><br>It has been an emotional and thrilling rollercoaster ride for the fans of the most [http://Mondediplo.com/spip.php?page=recherche&recherche=popular+team popular team] sport in the world. According to a June 3 MLS Brasil 2014 preview, Est. The trophy will travel to 83 countries in total as part of the FIFA World Cup Trophy Tour by Coca-Cola, spanning a total of 225 days covering 138,902 km in the process before arriving in South Africa on the 4th of May. We specialize in Sony Playstation 3, PS2, PSP, Nintendo Wii, DS and Microsoft xbox 360 offering fast delivery. March 17 vote by the Brazilian Football Association of South America the only country fighting for the right to host.<br><br>If you liked this article and also you want to get guidance about Fifa 15 Hack ([https://www.facebook.com/fifa15cheatsandhack get more info]) generously go to our website.
In [[mathematics|mathematical]] study of the [[differential geometry of curves]], the '''total curvature''' of an [[immersion (mathematics)|immersed]] [[plane curve]] is the [[integral]] of [[curvature]] along a curve taken with respect to [[arc length]]:
 
:<math>\int_a^b k(s)\,ds.</math>
 
The total curvature of a closed curve is always an integer multiple of 2π, called the '''index''' of the curve, or '''[[turning number]]''' – it is the [[winding number]] of the unit [[tangent vector]] about the origin, or equivalently the degree of the map to the [[unit circle]] assigning to each point of the curve, the unit velocity vector at that point. This map is similar to the [[Gauss map]] for surfaces.
 
==Comparison to surfaces==
 
This relationship between a local geometric invariant, the curvature, and a global [[topological invariant]], the index, is characteristic of results in higher-dimensional [[Riemannian geometry]] such as the [[Gauss–Bonnet theorem]].
 
== Invariance ==
According to the [[Whitney–Graustein theorem]], the total curvature is invariant under a [[regular homotopy]] of a curve: it is the degree of the [[Gauss map]]. However, it is not invariant under homotopy: passing through a kink (cusp) changes the turning number by 1.
 
By contrast, [[winding number]] about a point is invariant under homotopies that do not pass through the point, and changes by 1 if one passes through the point.
 
== Generalizations ==
[[File:Closed polygonal line.svg|thumb|A closed [[polygonal chain]], with total curvature&nbsp;2''π''.]]
A finite generalization is that the exterior angles of a triangle, or more generally any [[simple polygon]], add up to 360°&nbsp;=&nbsp;2''π'' radians, corresponding to a turning number of 1. More generally, [[polygonal chain]]s that do not go back on themselves (no 180° angles) have well-defined total curvature, interpreting the curvature as point masses at the angles.
 
The total curvature of a curve γ in a higher dimensional [[Euclidean space]] (equipped with its arclength parameterization) can be obtained by flattening out the [[tangent developable]] to γ into a plane, and computing the total curvature of the resulting curve. That is, the total curvature of a curve in ''n''-dimensional space is
 
:<math>\int_a^b \left|\gamma''(s)\right|\sgn \kappa_{n-1}(s)\,ds</math>
 
where κ<sub>''n''&minus;1</sub> is last Frenet curvature (the [[torsion of curves|torsion]] of the curve) and sgn is the [[signum function]].
 
The minimum total curvature of any three-dimensional curve representing a given [[Knot (mathematics)|knot]] is an [[knot invariant|invariant]] of the knot. This invariant has the value 2π for the unknot, but by the [[Fary–Milnor theorem]] it is at least 4π for any other knot.
 
==References==
*{{citation|first= Wolfgang|last=Kuhnel|title=Differential Geometry: Curves - Surfaces - Manifolds|publisher=American Mathematical Society|year=2005|edition=2nd|isbn=978-0-8218-3988-1}} (translated by Bruce Hunt)
*{{citation|title=On the Total Curvature of Knots|first=John W.|last=Milnor|authorlink=John Milnor|journal=Annals of Mathematics | series = Second Series|volume=52|year=1950|pages=248–257|jstor=1969467|doi=10.2307/1969467|issue=2}}
*{{cite arxiv|first=John M.|last=Sullivan|title=Curves of finite total curvature|year=2007|eprint=math/0606007|class=math.GT }}.
 
[[Category:Curves]]
[[Category:Curvature (mathematics)]]

Revision as of 12:48, 23 February 2014

They really do not appreciate the pastime, and they don't realize the magnitude or impact soccer has on the human race. There is no need to worry, If one does not have all the above characteristics, think success is not a heavenly fruit, as if one can only dream of it, everybody can achieve it with various techniques. You must watch the goal of season when he equals the highest number of goals in Spain. Also, he won the European cup thrice with Ajax and was voted European team player in 1999. The players wish to build a strong team of footballers who can easily snatch success from competitors.

2005 marked the milestone in Ronaldinho's career when he won the two prizes: European Footballer of the Year and FIFA World Player of the Year. The Forlan fan site started for him provides all the information's and the biography of him with his full history which can be viewed by any of his fan at any time. Later these teams went on to win round of 16 stage also and entered quarter finals. For goal scoring opportunities, the lobbed pass is the best option, and a lobbed ball is hard to block or intercept. For soccer fans watching this match on television, English broadcast will be provided by big ESPN (Direc - TV channel) at 2:30 p.

FIFA Soccer 11 is the latest soccer game developed by EA Sports. And last store them to a safe partition on computer. Those who are actually selling or farming coins will be banned from all EA games forever. In addition, Adidas also provided the game ball for the European Cup, Champions League and other games. However may fans of Donovan think it was a personal shot at the star.

The American foreigner ıs trained to an ally for soccer, and not a promoter. After retirement, Maradona spent most of his time in Cuba (can say in hospital), and after returning to Argentina suddently he suffered a major heart attack following a cocaine overdose and was admitted to intensive care in a Buenos Aires hospital. Xavi (Midfielder, Spain): If anyone would have watched you wins most season, his four awesome goals against archrivals Real Madrid in 2009, leading to the Barcelona club victory by 6-2, he would have enjoyed the contest thoroughly. We'll see if they can keep the momentum against Gabon next month. Iconic number 7's are David Villa, Raul Gonzalez, Franck Ribery, Luis Figo, George Best, Eric Cantona, Juanito, Amaro, David Beckham, Cristiano Ronaldo, Bastian Schweinsteiger and Andriy Schevchenko.

It has been an emotional and thrilling rollercoaster ride for the fans of the most popular team sport in the world. According to a June 3 MLS Brasil 2014 preview, Est. The trophy will travel to 83 countries in total as part of the FIFA World Cup Trophy Tour by Coca-Cola, spanning a total of 225 days covering 138,902 km in the process before arriving in South Africa on the 4th of May. We specialize in Sony Playstation 3, PS2, PSP, Nintendo Wii, DS and Microsoft xbox 360 offering fast delivery. March 17 vote by the Brazilian Football Association of South America the only country fighting for the right to host.

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