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| <!-- [[Image:Animated construction of butterfly curve.gif|left|thumb|150px|An animated construction gives an idea of the complexity of the [[curve]] (''Click for enlarged version'').]] -->
| | Oscar is what my spouse loves to contact me and I totally dig that title. Doing ceramics is what adore doing. North Dakota is exactly where me and my husband reside. For many years he's been working as a meter reader and it's something he really appreciate.<br><br>Also visit my webpage [http://nuvem.tk/altergalactica/AliceedMaurermy nuvem.tk] |
| [[Image:Butterfly trans01.svg|thumb|250px|The butterfly curve.]]
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| The '''butterfly curve''' is a [[Transcendental function|transcendental]] [[plane curve]] discovered by [[Temple H. Fay]]. The curve is given by the following [[parametric equation]]s:
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| :<math>x = \sin(t) \left(e^{\cos(t)} - 2\cos(4t) - \sin^5\left({t \over 12}\right)\right)</math>
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| :<math>y = \cos(t) \left(e^{\cos(t)} - 2\cos(4t) - \sin^5\left({t \over 12}\right)\right)</math>
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| or by the following [[polar equation]]:
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| :<math>r=e^{\cos \theta} - 2 \cos (4 \theta ) + \sin^5\left(\frac{2 \theta - \pi}{24}\right)</math>
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| {{clear}}
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| ==See also==
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| * [[Butterfly curve (algebraic)]]
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| ==References==
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| *{{cite journal
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| | first = Temple H.
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| | last = Fay
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| |date=May 1989
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| | title = The Butterfly Curve
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| | journal = Amer. Math. Monthly
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| | volume = 96
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| | issue = 5
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| | pages = 442–443
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| | doi = 10.2307/2325155
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| | jstor=2325155}}
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| *{{MathWorld|title=Butterfly Curve|urlname=ButterflyCurve}}
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| ==External links==
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| * An animation based on the butterfly curve: [http://www.freaknet.org/alpt/misc/ganim_video.avi video]. The script to reproduce it with gnuplot : [http://www.freaknet.org/alpt/src/misc/ganim.sh script]
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| [[Category:Curves]]
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| {{geometry-stub}}
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Latest revision as of 02:34, 25 November 2014
Oscar is what my spouse loves to contact me and I totally dig that title. Doing ceramics is what adore doing. North Dakota is exactly where me and my husband reside. For many years he's been working as a meter reader and it's something he really appreciate.
Also visit my webpage nuvem.tk