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[[File:Cycloid f.gif|right|frame|A cycloid generated by a rolling circle]]
A '''cycloid''' is the curve traced by a point on the rim of a circular wheel as the wheel rolls along a straight line.
It is an example of a [[roulette (curve)|roulette]], a curve generated by a curve rolling on another curve.


The inverted cycloid (a cycloid rotated by 180 °) is the solution to the [[brachistochrone problem]] (i.e., it is the curve of fastest descent under gravity) and the related [[tautochrone problem]] (i.e., the period of an object in descent without friction inside this curve does not depend on the object's starting position).
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{{quotebox|width=30%|
quote=It was in the left hand try-pot of the Pequod, with the soapstone diligently circling round me, that I was first indirectly struck by the remarkable fact, that in geometry all bodies gliding along the cycloid, my soapstone for example, will descend from any point in precisely the same time.
|source=[[Moby Dick]] by [[Herman Melville]], 1851}}


The cycloid has been called "The Helen of Geometers" as it caused frequent quarrels among 17th-century mathematicians.<ref>{{Cite book | last1=Cajori | first1=Florian | author1-link=Florian Cajori | title=A History of Mathematics | publisher=Chelsea | location=New York | isbn=978-0-8218-2102-2 | year=1999 | page=177 }}</ref>
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Historians of mathematics have proposed several candidates for the discoverer of the cycloid.  Mathematical historian [[Paul Tannery]] cited similar work by the Syrian philosopher [[Iamblichus]] as evidence that the curve was likely known in antiquity.<ref name=Tannery/>  English mathematician [[John Wallis]] writing in 1679 attributed the discovery to [[Nicholas of Cusa]],<ref name=Wallis/> but subsequent scholarship indicates Wallis was either mistaken or the evidence used by Wallis is now lost.<ref name=Whitman/>  [[Galileo Galilei]]'s name was put forward at the end of the 19th century<ref name=Cajori/> and at least one author reports credit being given to [[Marin Mersenne]].<ref name=Roidt/> Beginning with the work of [[Moritz Cantor]]<ref name=Cantor/> and Siegmund Günther,<ref name=Gunther/> scholars now assign priority to French mathematician [[Charles de Bovelles]]<ref name=Phillips/><ref name=Victor/><ref name=Martin/> based on his description of the cycloid in his ''Introductio in geometriam'', published in 1503.<ref name=Bovelles/>  In this work, Bovelles mistakes the arch traced by a rolling wheel as part of a larger circle with a radius 120% larger than the smaller wheel.<ref name=Whitman/>
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Galileo originated the term ''cycloid'' and was the first to make a serious study of the curve.<ref name=Whitman /> According to his student [[Evangelista Torricelli]],<ref name=Torricelli/> in 1599 Galileo attempted the [[Quadrature (mathematics)|quadrature]] of the cycloid (constructing a square with area equal to the area under the cycloid) with an unusually empirical approach that involved tracing both the generating circle and the resulting cycloid on sheet metal, cutting them out and weighing them. He discovered the ratio was roughly 3:1 but incorrectly concluded the ratio was an irrational fraction, which would have made quadrature impossible).<ref name=Roidt/> Around 1628, [[Gilles de Roberval|Gilles Persone de Roberval]] likely learned of the quadrature problem from [[Marin Mersenne|Père Marin Mersenne]] and effected the quadrature in 1634 by using [[Cavalieri's principle|Cavalieri's Theorem]].<ref name=Whitman />  However, this work was not published until 1693 (in his ''Traité des Indivisibles'').<ref name=Walker />
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Constructing the [[tangent]] of the cycloid dates to August 1638 when Mersenne received unique methods from Roberval, [[Pierre de Fermat]] and [[René Descartes]].  Mersenne passed these results along to Galileo, who gave them to his his students Torricelli and Viviana, who were able to produce a quadrature. This result and others were published by Torricelli in 1644,<ref name=Torricelli/> which is also the first printed work on the cycloid.  This led to Roberval charging Torricelli with plagiarism, with the controversy cut short by Torricelli's early death in 1647.<ref name=Walker />
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In 1658, Blaise Pascal had given up mathematics for theology but, while suffering from a toothache, began considering several problems concerning the cycloid.  His toothache disappeared, and he took this as a heavenly sign to proceed with his research. Eight days later he had completed his essay and, to publicize the results, proposed a contest.  Pascal proposed three questions relating to the [[Center of mass|center of gravity]], area and volume of the cycloid, with the winner or winners to receive prizes of 20 and 40 Spanish [[doubloon]]s. Pascal, Roberval and Senator Carcavy were the judges, and neither of the two submissions (by [[John Wallis]] and Antoine Lalouvère) were judged to be adequate.<ref name=Conner />{{rp|198}} While the contest was ongoing, [[Christopher Wren]] sent Pascal a proposal for a proof of the [[arc length|rectification]] of the cycloid; Roberval claimed promptly that he had known of the proof for years. Wallis published Wren's proof (crediting Wren) in Wallis's ''Tractus Duo'', giving Wren priority for the first published proof.<ref name=Walker />
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Fifteen years later, [[Christiaan Huygens]] had deployed the cycloidal pendulum to improve chronometers and had discovered that a particle would traverse an inverted cycloidal arch in the same amount of time, regardless of its starting point. In 1686, [[Gottfried Wilhelm Leibniz]] used analytic geometry to describe the curve with a single equation.  In 1696, [[Johann Bernoulli]] posed the [[brachistochrone curve|brachistochrone problem]], the solution of which is a cycloid.<ref name=Walker />
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[[File:Cycloid04.png|thumb|400px|A cycloid generated by a circle of radius ''r'' = 2]]
 
The cycloid through the origin, generated by a circle of radius ''r'', consists of the points (''x'', ''y''), with
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</ul>


Solving for ''t'' and replacing, the [[Cartesian coordinate system|Cartesian equation]] would be
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:<math>x = r \cos^{-1} \left(1 - \frac{y}{r}\right) - \sqrt{y(2r - y)}.</math>
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</ul>


The first arch of the cycloid consists of points such that
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:<math>0 \le t \le 2 \pi.</math>
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When ''y'' is viewed as a function of ''x'', the cycloid is [[differentiable]] everywhere except at the [[Cusp (singularity)|cusps]] where it hits the ''x''-axis, with the derivative tending toward <math>\infty</math> or <math>-\infty</math> as one approaches a cusp. The map from ''t'' to (''x'',&nbsp;''y'') is a differentiable [[curve]] or [[parametric curve]] of class ''C''<sup>∞</sup> and the singularity where the derivative is 0 is an ordinary cusp.
== Ugg Boots Nz  Delivery/Time ==


The cycloid satisfies the [[ordinary differential equation|differential equation]]:
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:<math>\left(\frac{dy}{dx}\right)^2 = \frac{2r}{y} - 1.</math>
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==Evolute==
 
[[File:Evolute generation.png|thumb|Generation of the evolute of the cycloid unwrapping a tense wire placed on half cycloid arc (red marked)]]
  <li>[http://new.mg666.com/forum.php?mod=viewthread&tid=1050203 http://new.mg666.com/forum.php?mod=viewthread&tid=1050203]</li>
The [[Evolute]] of the Cycloid has the property to be exactly the same cycloid it originates from. This can otherwise be seen from the fact that the tip of a wire initially laying on an half arc of cycloid describes a cycloid arc equal to the one he was laying on once unwrapped (see also [[Cycloid#Cycloidal pendulum|Cycloidal pendulum]] and [[Cycloid#Arc length|Arc length]]).
 
===Demonstration===
  <li>[http://scottalanciolek.com/Main_Page http://scottalanciolek.com/Main_Page]</li>
[[File:Evolute demo.png|thumb|Demonstration of the properties of the evolute of a cycloid]]
 
There are several demonstrations of the assertion. The one presented here uses the physical definition of cycloid and the cinematic property that the instantaneous velocity of a point is tangent to its trajectory.
  <li>[http://cgi.www5c.biglobe.ne.jp/~kk_aoi/bbs/apeboard_plus.cgi/ http://cgi.www5c.biglobe.ne.jp/~kk_aoi/bbs/apeboard_plus.cgi/]</li>
Referring to the picture on the right, be P1 and P2 two tangent points belonging to two rolling circles. The two circles start to roll with same speed and same direction without skidding. P1 and P2 start to draw two cycloid arcs as in the picture. Considering the line connecting P1 and P2 at an arbitrary istant (red line) it is possible to prove that ''the line is anytime tangent in P2 to the lower arc and orthogonal to the tangent in P1 of the upper arc''. In fact we see that:
 
*P1, Q and P2 are aligned because <math>\widehat{P1O1Q}=\widehat{P2O2Q}</math> (equal rolling speed) and therefore <math>\widehat{O1QP1}=\widehat{O2QP2}</math>. Since <math>\widehat{O1QP2}+\widehat{O2QP2}=\pi</math> by construction it follows <math>\widehat{P1QP2}=\pi</math>.
  <li>[http://www.siksik-immobilier.com/spip.php?article303 http://www.siksik-immobilier.com/spip.php?article303]</li>
*If A is the meeting point between the perpendicular from P1 to the straight of O1O2 and the tangent to the circle in P2 then the triangle P1AP2 is isosceles because <math>\widehat{QP2A}=\frac{1}{2}\widehat{P2O2Q}</math> and <math>\widehat{QP1A}=\frac{1}{2}\widehat{QO1R}=</math>(easy to prove seen the construction)<math>=\frac{1}{2}\widehat{QO1P1}</math>.For the previous noted equality between <math>\widehat{P1O1Q}</math> and <math>\widehat{QO2P2}</math> then <math>\widehat{QP1A}=\widehat{QP2A}</math> and P1AP2 is isosceles.
 
*Conducting from P2 the orthogonal straight to O1O2, from P1 the straight line tangent to the upper circle and calling B the meeting point is now easy to see that P1AP2B is a [[Rhombus]], using the theorems concerning the angles between parallel lines
</ul>
*Now let's consider the speed V2 of P2. It can be seen as the sum of 2 components, the rolling speed Va and the Drifting speed Vd.Both speeds are equal in modulus because the circles rolls without skidding.Vd is parallel to P1A and Va is tanget to the lower circle in P2 therefore is parallel to P2A.The total speed of P2, V2 is then parallel to P2P1 because both are diagonals of two rhombuses with parallel sides and has in common with P1P2 the contact point P2. It follows that the speed vector V2 lies on the prolongation of P1P2. Because V2 is tangent to the arc of cycloid in P2 it follows that also P1P2 is tangent.
*Analogously it can be easily demonstrated that P1P2 is orthogonal to V1 (other diagonal of the rhombus).
* The tip of an inextensible wire initially stretched on half arc of cycloid and bounded to the upper circle in P1 will then follow the point along its path ''without changing its length'' because the speed of the tip is at each moment orthogonal to the wire (no stretching or compression). The wire will be at the same time tangent in P2 to the lower arc because the tension and the demonstrated items . If it would not be tangent then there would be a discontinuity in P2 and consequently there would be unbalanced tension forces.
 
== Area ==
One arch of a cycloid generated by a circle of radius ''r'' can be parameterized by
 
:<math>\begin{align}
  x &= r(t - \sin t) \\
  y &= r(1 - \cos t)
\end{align}</math>
 
with
<math>\frac{dx}{dt} = r(1 - \cos t)</math>
:<math>0 \le t \le 2 \pi.</math>
 
Since
 
:<math>\frac{dx}{dt} = r(1 - \cos t)</math>
 
the area under the arch is
 
:<math>\begin{align}
  A &= \int_{t=0}^{t=2 \pi} y \, dx = \int_{t=0}^{t=2 \pi} r^2(1 - \cos t)^2 dt \\
    &= \left. r^2 \left(\frac{3}{2}t - 2\sin t + \frac{1}{2} \cos t \sin t\right) \right|_{t=0}^{t=2\pi} \\
    &= 3 \pi r^2.
\end{align}</math>
 
== Arc length ==
[[File:Cycloid length.png|thumb|The length of the cycloid as consequence of the property of its evolute]]
The arc length ''S'' of one arch is given by
:<math>\begin{align}
  S &= \int_0^{2\pi} \left[\left(\frac{\operatorname d\!y}{\operatorname d\!t}\right)^2 + \left(\frac{\operatorname d\!x}{\operatorname d\!t}\right)^2\right]^\frac{1}{2} \operatorname d\!t \\
    &= \int_0^{2\pi} r \sqrt{2 - 2\cos(t)}\, \operatorname d\!t \\
    &= \int_0^{2\pi} 2\,r \sin \frac{t}{2}\, \operatorname d\!t \\
    &= 8\,r.
\end{align}
</math>
 
Another immediate way to calculate the length of the cycloid given the properties of the [[Cycloid#Evolute|Evolute]] is to notice that when a wire describing an evolute has been completely unwrapped it extends itself along 2 diameters that means 4r. Because the wire do not change length during the unwrapping it follows that the length of half an arc of cycloid is 4r and a complete arc is 8r.
 
== Cycloidal pendulum ==
{{Expand section|date=December 2009}}
[[File:CyloidPendulum.png|right|thumb|Schematic of a cycloidal pendulum.]]
If a simple pendulum is suspended from the cusp of an inverted cycloid, such that the "string" is constrained between the adjacent arcs of the cycloid, and the pendulum's length is equal to that of half the arc length of the cycloid (i.e., twice the diameter of the generating circle), the bob of the [[pendulum]] also traces a cycloid path. Such a cycloidal pendulum is [[Tautochrone curve|isochronous]], regardless of amplitude. The equation of motion is given by:
 
:<math>\begin{align}
  x &= r[\theta(t) - \sin \theta (t)] \\
  y &= r[\cos \theta (t) - 1].
\end{align}</math>
 
The 17th-century Dutch mathematician [[Christiaan Huygens#Clocks|Christiaan Huygens]] discovered and proved these properties of the cycloid while searching for more accurate pendulum clock designs to be used in navigation.<ref>C. Huygens, "The Pendulum Clock or Geometrical Demonstrations Concerning the Motion of Pendula (sic) as Applied to Clocks," Translated by R. J. Blackwell, Iowa State University Press (Ames, Iowa, USA, 1986).</ref>
 
== Related curves ==
Several curves are related to the cycloid.
* '''Curtate cycloid''': Here the point tracing out the curve is inside the circle, which rolls on a line.
* '''Prolate cycloid''': Here the point tracing out the curve is outside the circle, which rolls on a line.
* '''[[Trochoid]]''': refers to any of the cycloid, the curtate cycloid and the prolate cycloid.
* '''[[Hypocycloid]]''': The point is on the edge of the circle, which rolls not on a line but on the inside of another circle.
* '''[[Epicycloid]]''': The point is on the edge of the circle, which rolls not on a line but on the outside of another circle.
* '''[[Hypotrochoid]]''': As hypocycloid but the point need not be on the edge of its circle.
* '''[[Epitrochoid]]''':  As epicycloid but the point need not be on the edge of its circle.
 
All these curves are [[roulette (curve)|roulettes]] with a circle rolled along a uniform [[curvature]]. The cycloid, epicycloids, and hypocycloids have the property that each is [[Similarity (geometry)|similar]] to its [[evolute]]. If ''q'' is the [[product (mathematics)|product]] of that curvature with the circle's radius, signed positive for epi- and negative for hypo-, then the curve:evolute [[Homothety|similitude ratio]] is 1&nbsp;+&nbsp;2''q''.
 
The classic [[Spirograph]] toy traces out hypotrochoid and [[epitrochoid]] curves.
 
== Use in architecture ==
[[File:Kimbell Art Museum.jpg|thumb|Cycloidal arches at the [[Kimbell Art Museum]]]]
 
The cycloidal arch was used by architect [[Louis Kahn]] in his design for the [[Kimbell Art Museum]] in [[Fort Worth, Texas]]. It was also used in the design of the [[Hopkins Center for the Arts|Hopkins Center]] in [[Hanover, New Hampshire]].
 
== Use in violin plate arching ==
Early research indicated that some transverse arching curves of the plates of golden age violins are closely modeled by curtate cycloid curves.<ref>{{cite journal|last=Playfair|first=Q|title=Curtate Cycloid Arching in Golden Age Cremonese Violin Family Instruments|journal=Catgut Acoustical Society Journal|volume=4|series=II|issue=7|pages=48–58}}</ref> Later work indicates that curate cycloids do not serve as general models for these curves,<ref>{{cite journal|last=Mottola|first=RM|title=Comparison of Arching Profiles of Golden Age Cremonese Violins and Some Mathematically Generated Curves|journal=Savart Journal|year=2011|volume=1|issue=1|url=http://savartjournal.org/index.php/sj/article/view/12}}</ref> which vary considerably.
 
== See also ==
* [[List of periodic functions]]
* [[Epicycloid]]
* [[Epitrochoid]]
* [[Hypocycloid]]
* [[Hypotrochoid]]
* [[Spirograph]]
* [[Tautochrone curve]]
 
== References ==
{{reflist | refs=
 
<ref name=Conner>
{{citation
| last=Conner
| first=James A.
| title=Pascal's Wager: The Man Who Played Dice with God
| pages=224
| ISBN=9780060766917
| edition=1st
| year=2006
| publisher=HarperCollins
}}</ref>
 
<ref name=Torricelli>
{{citation
| last=Torricelli
| first=Evangelista
| title=Opera geometrica
| year=1644
| OCLC=55541940
}}
</ref>
 
<ref name=Phillips>
{{citation
| title=Brachistochrone, Tautochrone, Cycloid&mdash;Apple of Discord
| last=Phillips
| first=J. P.
| journal=The Mathematics Teacher
| volume=60
| number=5
| month=May
| year=1967
| pages=506&ndash;508
| url=http://www.jstor.org/stable/27957609
}}{{subscription required}}
</ref>
 
<ref name=Gunther>
{{citation
| title=Vermischte untersuchungen zur geschichte der mathematischen wissenschaften
| last=Günther
| first=Siegmund
| year=1876
| location=Leipzig
| publisher=Druck und Verlag Von B. G. Teubner
| OCLC=2060559
| pages=352
}}
</ref>
 
<ref name=Wallis>
{{cite doi|10.1098/rstl.1695.0098}} (Cited in Günther, p. 5)
</ref>
 
<ref name=Cajori>
{{citation
| last=Cajori
| first=Florian
| title=A History of Mathematics
| url=http://books.google.com/books?id=mGJRjIC9fZgC
| edition=5th
| ISBN=0-8218-2102-4
| page=162
}}(Note:  The [http://books.google.com/books?id=kqQPAAAAYAAJ first (1893) edition] and its reprints state that Galileo invented the cycloid.  According to Phillips, this was corrected in the second (1919) edition and has remained through the most recent (fifth) edition.)
</ref>
 
<ref name=Bovelles>
{{citation
| title=Introductio in geometriam ... Liber de quadratura circuli. Liber de cubicatione sphere. Perspectiva introductio.
| last=de Bouelles
| first=Charles
| year=1503
| OCLC=660960655
}}
</ref>
 
<ref name=Victor>
{{citation
| title=Charles de Bovelles, 1479-1553:  An Intellectual Biography
| last=Victor
| first=Joseph M.
| url=http://books.google.com/books?hl=en&lr=&id=bw4lM9wF1lgC
| page=42
| year=1978
| ISBN=978-2-600-03073-1
}}
</ref>
 
<ref name=Martin>
{{cite doi
|10.4169/074683410X475083
}}
</ref>
 
<ref name=Cantor>
{{citation
| title=Vorlesungen über Geschichte der Mathematik, Bd. 2
| last=Cantor
| first=Moritz
| publisher=B. G. Teubner
| location=Leipzig
| year=1892
| url=http://archive.org/details/vorlesungenuberg00cant
| OCLC=25376971
}}
</ref>
 
<ref name=Roidt>
{{cite thesis
| title=Cycloids and Paths
| last=Roidt
| first=Tom
| year=2011
| type=MS
| page=4
| url=http://www.web.pdx.edu/~caughman/Cycloids%20and%20Paths.pdf
| publisher=Portland State University
}}
</ref>
 
<ref name=Whitman>
{{citation
| title=Some historical notes on the cycloid
| journal=The American Mathematical Monthly
| volume=50
| number=5
| date=May 1943
| pages=309&ndash;315
| url=http://www.jstor.org/stable/2302830
| last=Whitman
| first=E. A.
}} {{subscription required}}</ref>
 
<ref name=Tannery>
{{citation
| last=Tannery
| first=Paul
| title=Pour l'histoire des lignes et surfaces courbes dans l'antiquité
| journal=Bulletin des sciences mathèmatique
| location=Paris
| year=1883
| page=284
}} (cited in Whitman 1943); 
</ref>
 
<ref name=Walker>
{{citation
| last=Walker
| first=Evelyn
| title=A Study of Roberval's Traité des Indivisibles
| publisher=Columbia University
| year=1932
}} (cited in Whitman 1943);
</ref>
 
}}
 
== Further reading ==
{{Reflist}}
* ''An application from physics'': Ghatak, A. & Mahadevan, L. Crack street: the cycloidal wake of a [[cylinder (geometry)|cylinder]] tearing through a sheet. Physical Review Letters, 91, (2003). [http://link.aps.org/abstract/PRL/v91/e215507 link.aps.org]
* Edward Kasner & James Newman (1940) [[Mathematics and the Imagination]], pp 196&ndash;200, [[Simon & Schuster]].
* {{cite book | author = Wells D | year = 1991 | title = The Penguin Dictionary of Curious and Interesting Geometry | publisher = Penguin Books | location = New York | isbn = 0-14-011813-6 | pages = 445–47}}
 
== External links ==
* {{MacTutor | class=Curves | id=Cycloid | title=Cycloid}}
* {{MathWorld | urlname=Cycloid | title=Cycloid}} Retrieved April 27, 2007.
* [http://www.cut-the-knot.org/pythagoras/cycloids.shtml Cycloids] at [[cut-the-knot]]
* [http://historical.library.cornell.edu/cgi-bin/cul.math/docviewer?did=02260001&seq=9 A Treatise on The Cycloid and all forms of Cycloidal Curves], monograph by Richard A. Proctor, B.A. posted by [http://historical.library.cornell.edu/math/index.html Cornell University Library].
* ''[http://demonstrations.wolfram.com/CycloidCurves/ Cycloid Curves]'' by Sean Madsen with contributions by David von Seggern, [[Wolfram Demonstrations Project]].
* [http://communities.ptc.com/videos/2077 Cycloid on PlanetPTC (Mathcad]
 
[[Category:Curves]]

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It like being with your mates down the pub and spouting crap. And you can swear all you want too, just like in real life.So, I would like to express gratitude to all of you who read every single day, who contribute and who've helped to make Arseblog what it is today.

EDIT: I had an idea but its a longshot and means you have to fit a soundcard. I know it's a slim case, but I can consider one sound card that might fit it. That comes with a changeable backplate to permit it to fit HTPC cases which are a lot narrower. You PC may have a PCI express slot if it's Ray Ban Sunglasses Canada not that old. I'm sure that would ignore the fact that you fitted a card instead of accept they have mislead you. (assuming the manual on yours reads the same)

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Warning: date(): It's not safe to rely on the system's timezone settings. In case you used any of those methods and you're still getting this warning, you almost certainly misspelled the timezone identifier. In case you used those methods and you are still getting this warning, you most likely misspelled the timezone identifier. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier. In case you used any of those methods and you are still getting this warning, you almost certainly misspelled the timezone identifier. In case you Polo Ralph Lauren Toronto used those methods and you are still getting this warning, you almost certainly misspelled the timezone identifier. In case you used those methods and you are still getting this warning, you almost certainly misspelled the timezone identifier. In case you used any of those methods and you are still getting this warning, you almost certainly misspelled the timezone identifier. In case you used those methods and you are still getting this warning, you most likely misspelled the timezone identifier. In case you used those methods and you are still getting this warning, you almost certainly misspelled the timezone identifier. In case you used any of those methods and you are still getting this warning, you almost certainly misspelled the timezone identifier. In case you used those methods and you are still getting this warning, you most likely misspelled the timezone identifier. In case you used any of those methods and you are still getting this warning, you most likely misspelled the timezone identifier.

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You may also learn more about the Air Max 1 references Dr. Jill cites inher book and lectures about the different characteristics in the leftand right hemispheres.An explanation of the right and left hemispheresHave you experienced a stroke or any other health issue? Are you a caregiver to a person who inspires you using their strength and courage? Share your story to be a "Stroke Triumphant" and inspire others to find their way.Showered with love and ready for recovery!Do you practice yoga or meditate? What different techniques do you use to "Step to the Right" of the left hemisphere brain chatter in order to live a more balanced life? Share your ideas in the Balanced Brain Techniques page.Neural Processing by Jill Bolte Taylor 2007The stories of insight derive from Dr.

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Measured from the seawall because that was the mean high water line that a 19year engineering calculation, he said. are going to measure again in the water edge to see if we move forward. It could mean a difference of 200 feet. He also points to a letter from Secretary of State Delbert Hosemann towards the commission that he believes supports the seawall boundary. The Secretary of State Office oversees public trust tidelands, the area between the seawall and where the water meets the shore. El born area is owned by the state in trust as public tidelands. Businesses locating in this area must lease the land in the state.

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Only the L 40 dike and canal is going to be closed from around the gate area. Celebrate Parks and Recreation Month July is Parks and Recreation Month, so it's a great time to explore the many fun and educational opportunities that can be found in Florida's 160 state parks. Activities change from hiking and picnicking to fishing, Hollister Canada swimming or using a playground.

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The ZCFC Card does not have a normal Display Port, instead it has two Mini Display Ports which I do not have an adapter for. I also get the feeling that you may not require to use an active adapter for these Mini Display Ports. ( Just the way it talks about them on the box. I cold be wrong though ).

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However it does not give us fun, engaging speaking tasks. A minimum of, most coursebooks don which is unfortunate since most students sign up for ESL classes to understand to speak English. However, because we're Ray Ban Aviators resourceful teachers, we can always give you the engaging speaking tasks that coursebooks seem to be missing.

We know from a previous report that GeForce GTX 780 will be positioned a notch below the GeForce GTX TITAN, in NVIDIA's product stack. It may be based on the same GK110 silicon, and may feature 2,496 CUDA cores, and a 320 bit wide GDDR5 memory interface, holding 5 GB of memory. It's not going to surprise us if NVIDIA completely recycles the GTX TITAN PCB, because it doesn't particularly have an over the top selection of components, apart from the GPU. The GeForce GTX 770 is really a different beast altogether. It is based on a GPU not unlike the GK104, with 1,536 CUDA cores, along with a 256 bit wide GDDR5 memory interface, holding 4gb of memory. To sweeten the prospect of upgrading to these new cards, NVIDIA is looking at the same sexy magnesium alloy based cooling solution it used on $1000 cards such as the GTX TITAN and GTX 690.

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Maybe we "Westerners" have a bit of a nerve to denounce the destruction of Syria's antiquity. In the Roman destruction of Carthage to RAF Bomber Command's pounding of Hamburg, Dresden along with a hundred medieval German cities to rubble, we've been smashing our history to bits for hundreds of years. The pillaging of Europe's great cities would be a practice of war as common as the rape of an enemy's womenfolk for years and years, and the last century has witnessed such savagery on an unprecedented scale. The German destruction of the Louvain library and the Cloth Hall of Ypres and countless French Gothic cathedrals and churches in the First World War, to the bombing of Rotterdam, the City of London, Coventry and Canterbury and also the great cities of Germany not to mention the priceless monastery of Monte Cassino we're in no position to suggest the finger at the Arab world for its historical self immolation.

The White House recently unveiled plans for any new Digital Promise research center which will support the development of educational software along Ralph Lauren Canada with other instructional technologies. Department of Education, will be supported by a large number of businesses and non profit organizations. Former FCC Chairman Newton Minow and former NBC News President Lawrence Grossman spearheaded the movement to form the center, which is officially known as the National Center for Research in Advanced Information and Digital Technologies. Greater than 50 years ago, Minor referred to commercial television as "a vast wasteland." Today he's looking forward to the promises of digital technology in schools.

"[Alternatively,] all the West has to do is follow Putin's ways. He assassinates his enemies without blinking a watch. Assassinate the four or five Mullahs who run the show, Ahmadinejad and a few more Iranian fanatics, and the War can be avoided. It might be difficult to do, but not impossible. With today's hi tech technology I am Air Max 1 sure that new weapons against individuals are being prepared right now. I think it would be a better way of handling the problem than an all out war against Islam."

Their arrest on charges of impeding the investigation into the Boston Marathon bombings to help their friend, prime suspect Dzhokhar Tsarnaev, left many within the huge former Soviet republic in disbelief.Tazhayakov had enjoyed a privileged upbringing, attending a top-notch school in the capital Astana. Kadyrbayev had thought it was harder at school in the commercial capital Almaty but was delighted when he got the grades to review in the United States.Although Kadyrbayev listed Islam as his world take Nike Air Max 1 on what appears to be his social media site, nothing obvious marked either out as Nike Roshe Run Toronto somebody who might one day help a suspected bomber."He studied for a year.

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Attack party leader Volen Siderov blamed the "colonial" West for low wages and high prices in Bulgaria, which joined europe in 2007 and has committed to budget restrictions and a currency peg in order to swap its lev for the single European currency used by 17 other EU member nations.

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The new NVIDIA GeForce GTX TITAN starts off strong in one of the most graphically intensive games out right now, Far Cry 3. I never utilize it but always know where it is. Also, how do we decide whetehr we need to backfill it with vermiculite? The first installer said not to and the other two didn't bring it up!! Agghhh!!! Any help appreciated please..

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Green Bank Leisure Centre, in Swadlincote, Derbyshire will get 150,000 of National Lottery funding to modernise its facilities. We were also able to have 4X MSAA, yes 4X MSAA, enabled at 5760x1200 with the highest ingame settings. As i said earlier it's AGM season coming up soon, time to marshal the forces of those wishing to retain this campsite and get yourselves elected onto the County Exec and be sure you form the majority which may well require voting off existing members who've voted for the campsite to be removed.

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