Witch of Agnesi

A curve studied and named ``versiera'' (Italian for ``she-devil'' or ``witch'') by Maria Agnesi in 1748 in her book Istituzioni Analitiche (MacTutor Archive). It is also known as Cubique d'Agnesi orAgnésienne. Some suggest that Agnesi confused an old Italian word meaning ``free to move'' withanother meaning ``witch.'' The curve had been studied earlier by Fermat and Guido Grandi in 1703.

It is the curve obtained by drawing a line from the origin through the Circle of radius (), then picking thepoint with the coordinate of the intersection with the circle and the coordinate of the intersection of the extensionof line with the line . The curve has Inflection Points at . The line is an Asymptote to the curve.

In parametric form,

			(1)
			(2)

			(3)
			(4)

(5)

References

Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 90-93, 1972.

Lee, X. ``Witch of Agnesi.''http://www.best.com/~xah/SpecialPlaneCurves_dir/WitchOfAgnesi_dir/witchOfAgnesi.html

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

Yates, R. C. ``Witch of Agnesi.'' A Handbook on Curves and Their Properties. Ann Arbor, MI: J. W. Edwards, pp. 237-238, 1952.

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