|Back to . . .||This derivation . . .
uses similar triangles and the Pythagorean Theorem. While no advanced mathematical concepts are required, the curve provides excellent preparation for studying the calculus of variations. Let A move along line QA. Segment OA changes. The intersection of segment OA and the Circle at B also changes. Now focus on point P.
|Any point Pon the "witch" is located by constructing lines parallel to the x and yaxes through Band A respectively and determining the point P of intersection. The parallel lines are tangent to the circle.|
For further explanation, please see the MAA's College Mathematics Journal.
Gray, S. I. B. and Malakyan, Tagui (September, 1999). The Witch
of Agnesi: A Lasting Contribution from the First Surviving Mathematical
Work Written by a Woman. A commemorative on the 200th anniversary
of her death. College Mathematics Journal, Vol. 30, No.4, 258 -
for a brief review. Search under MAA Journals, Agnesi and 1999.