witch of Agnesi

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witch of Agnesi
A segment drawn from the origin to A intersects a circle of radius a at B. The witch of Agnesi is the curve formed by P as A moves along the line C.

witch of Ag·ne·si

A planar cubic curve that is symmetric about the y-axis and that approaches the x-axis as an asymptote. Its equation is x2y = 4a2(2a - y), where a is a constant.

[witch (translation of Italian avversiera, versiera, confused with versiera, curve, turning, from New Latin versōria, from Latin versus, turned, reversed, past participle of vertere, to turn; see verse1) + Maria Gaetana Agnesi.]
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

witch of Agnesi

(Mathematics) maths a plane curve, symmetrical about the y-axis, having the equation x2y = 4a2(2ay). Sometimes shortened to: witch
[C19: named after Maria Gaetana Agnesi (1718–99), Italian mathematician and philosopher; probably so called from the resemblance of the curve to the outline of a witch's hat]
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014
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The witch of Agnesi. The Journal of Recreational Mathematics, 1, 49-53.
In celebration of the 296th birthday of the famous female mathematician and philosopher Maria Gaetana Agnesi, Google treats visitors on the search engine homepage with an animated doodle on the "Witch of Agnesi."
For the arch and toe region, the simplest form of the Witch of Agnesi (WA) equation (Equation (1)) was used as a starting point for describing the corresponding nonlinear profile of the shoe insole curves: