A curve also known as the Gerono Lemniscate. It is given by Cartesian Coordinates

(1) |

(2) |

(3) | |||

(4) |

The Curvature and Tangential Angle are

(5) | |||

(6) |

**References**

Cundy, H. and Rollett, A. *Mathematical Models, 3rd ed.* Stradbroke, England: Tarquin Pub., p. 71, 1989.

Lawrence, J. D. *A Catalog of Special Plane Curves.* New York: Dover, pp. 124-126, 1972.

Lee, X. ``Lemniscate of Gerono.'' http://www.best.com/~xah/SpecialPlaneCurves_dir/LemniscateOfGerono_dir/lemniscateOfGerono.html.

MacTutor History of Mathematics Archive. ``Eight Curve.'' http://www-groups.dcs.st-and.ac.uk/~history/Curves/Eight.html.

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1999-05-25