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GXWeb Witch of Agnesi
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GXWeb Curve Construction Collection (like this one!)
About the Witch of Agnesi (from Wolfram MathWorld)
\(a\) 0 0 10 \(r\) 0 0 10 \(\theta\) 0 0 6.283
The Witch of Agnesi is a cubic plane curve defined from two diametrically opposite points of a circle. It gets its name from Italian mathematician Maria Gaetana Agnesi, and from a mistranslation of an Italian word for a sailing sheet. Before Agnesi, the same curve was studied by Fermat, Grandi, and Newton.
The Witch of Agnesi constructed here is the locus of point D where
\(a = Length(OE)\)
\(r = Length(OB) = Length(AB)\)
and \(angle(OBA) = \theta\).
Cartesian equation: \[X·Y^2+X·a^2-2·a^2·r\]
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