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In mathematics, the Witch of Agnesi ((:a.ˈɲe.zi)), sometimes called the Witch of Maria Agnesi is the curve defined as follows. 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 to 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 of Agnesi. The curve is asymptotic to the line tangent to the fixed circle through the point O. ==Equations== Suppose the point O is the origin, and that M is on the positive ''y''-axis. Suppose the radius of the circle is ''a''. Then the curve has Cartesian equation : Note that if ''a'' = 1/2, then this equation becomes rather simple: : This is the derivative of the arctangent function. Parametrically, if is the angle between OM and OA, measured clockwise, then the curve is defined by the equations : Another parameterization, with being the angle between OA and the ''x''-axis, increasing anti-clockwise is : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Witch of Agnesi」の詳細全文を読む スポンサード リンク
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