Friday, February 10, 2012

Plane Curves: Witch of Agnesi

Witch of Agnesi

The "witch of Agnesi" is a curve studied by Maria Agnesi in 1748 in her book Instituzioni analitiche ad uso della giovent? italiana (the first surviving mathematical work written by a woman). The curve is also known as cubique d'Agnesi or agnesienne, and had been studied earlier by Fermat and Guido Grandi in 1703. The name "witch" derives from a mistranslation of the term averisera ("versed sine curve," from the Latin vertere, "to turn") in the original work as avversiera ("witch" or "wife of the devil") in an 1801 translation of the work by Cambridge Lucasian Professor of Mathematics John Colson (Gray). Starting with a fixed circle, a point O on the circle is chosen. For any other point A on the circle, the secant line OA is drawn. The point M is diametrically opposite O. The line OA intersects the tangent of M at the point N. The line parallel to OM through N, and the line perpendicular to OM through A intersect at P. As the point A is varied, the path of P is the witch. The curve is asymptotic to the line tangent to the fixed circle through the point O.

Get copyable formulas for Witch of Agnesi from Differential Geometry Library (MathML, TeX, Mathematica input, Maple input)

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