The Witch of Agnesi
Author: Steve Arnold
Date: 19/06/06

What is the fascination with this famous curve? Can you deduce its construction? Can you find the equation which defines it?

Let P be the point (x, y) and the diameter of the circle be a. Let B be the point (t, y) - can you find the other points, and use these to find the function?

Use the point B to trace around the circle and so produce the curve.

Drag me around the circle!

Control the circle radius

The Witch of Agnesi

a = 4 (slider from 0 to 10, step 0.05)
A: (0, a)
c = Circle((0, a / 2), a / 2)
B = Point(c)
O = (0, 0)
b = Ray(O, B)
d = OrthogonalLine(B, yAxis)
e = OrthogonalLine(A, yAxis)
C = Intersect(b, e)
f = OrthogonalLine(C, xAxis)
P = Intersect(d, f)
Q, p, b_1, c_1 = Polygon(B, C, P)
f1(x) = a³ / (x² + a²)
D = (3.5, 1)
u = Vector(D, B)
E = (1, 8)
F = (5.5, 8)
G = (5.5, 6.5)
H = (1, 6.5)
R, e_1, f_1, g, h = Polygon(E, F, G, H)