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) |
See also Butterfly Curve, Dumbbell Curve, Eight Surface, Piriform
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.