Hessian form of an elliptic curve: Difference between revisions

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A '''serpentine curve''' is a curve whose equation is of the form
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<math>x^2y+a^2y-abx=0</math>, where <math>ab > 0</math>. Equivalently, it has a parametric representation <math>x=a\cot(t)</math>, <math>y=b\sin (t)\cos(t)</math>, or functional representation <math>y=\frac{abx}{x^2+a^2}</math>. Serpentine curves were studied by [[Guillaume de l'Hôpital|L'Hôpital]] and [[Christiaan_Huygens|Huygens]], and named and classified by [[Isaac Newton|Newton]].
[[Image:Serpentine curve.png|center|thumb|400px|The serpentine curve for <math>a=b=1.</math>]]
 
==External links==
* [http://mathworld.wolfram.com/SerpentineCurve.html MathWorld - Serpentine Equation]
* [http://www-groups.dcs.st-and.ac.uk/~history/Curves/Serpentine.html]
 
{{geometry-stub}}
 
[[Category:Curves]]

Latest revision as of 19:30, 31 October 2014

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