## Eight Curve

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

 (1)

Polar Coordinates,
 (2)

and parametric equations
 (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.