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| {{unreferenced|date = June 2012}}
| | Irwin Butts is what my wife enjoys to contact me though I don't truly like becoming called like that. For many years he's been operating as a receptionist. Years in the past we moved to North Dakota. Body developing is one of the issues I adore most.<br><br>Feel free to surf to my web page ... [http://www.youronlinepublishers.com/authWiki/AudreaocMalmrw at home std test] |
| [[Image:NegativePedal.gif|500px|right|thumb|[[Circle]] — negative pedal curve of a [[limaçon]]]]
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| In [[geometry]], a '''negative pedal curve''' is a [[plane curve]] that can be constructed from another plane curve ''C'' and a fixed point ''P'' on that curve. For each point ''X'' ≠ ''P'' on the curve ''C'', the negative pedal curve has a [[tangent]] that passes through ''X'' and is [[perpendicular]] to line ''XP''. Constructing the negative pedal curve is the [[inverse operation]] to constructing a [[pedal curve]].
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| ==Definition==
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| In the plane, for every point ''X'' other than ''P'' there is a unique line through ''X'' perpendicular to ''XP''. For a given curve in the plane and a given fixed point ''P'', called the '''pedal point''', the '''negative pedal curve''' is the [[envelope (mathematics)|envelope]] of the lines ''XP'' for which ''X'' lies on the given curve.
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| ==Parameterization==
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| For a parametrically defined curve, its negative pedal curve with pedal point (0; 0) is defined as
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| :<math>X[x,y]=\frac{(x^2-y^2)y'-2xyx'}{xy'-yx'}</math>
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| :<math>Y[x,y]=\frac{(x^2-y^2)x'+2xyy'}{xy'-yx'}</math>
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| ==Properties==
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| The negative pedal curve of a [[pedal curve]] with the same pedal point is the original curve.
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| ==External links==
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| * [http://mathworld.wolfram.com/NegativePedalCurve.html Negative pedal curve on Mathworld]
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| {{Differential transforms of plane curves}}
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| {{DEFAULTSORT:Negative Pedal Curve}}
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| [[Category:Curves]]
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| [[Category:Differential geometry]]
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Latest revision as of 14:44, 5 July 2014
Irwin Butts is what my wife enjoys to contact me though I don't truly like becoming called like that. For many years he's been operating as a receptionist. Years in the past we moved to North Dakota. Body developing is one of the issues I adore most.
Feel free to surf to my web page ... at home std test