Osculating Circle of Serpentine

 x = a cot t

           y = b sin t cos t

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References

• J. Dennis Lawrence, A Catalog of Special Plane Curves, pp. 111-112.

• 2d Curves : http://www.2dcurves.com/cubic/cubicse.html

• Math World : http://mathworld.wolfram.com/SerpentineCurve.html

• Jen-Chung Chuan : http://steiner.math.nthu.edu.tw/ne01/tjy/dynamic/contants/FamousCurves-e.html

• Famous Curves Index : http://www-gap.dcs.st-and.ac.uk/~history/Curves/Serpentine.html