Erkundung aller Fälle von x^3 = p x + q
Author: Prof. Dr. Dörte Haftendorn
Date: 8 Juni 2011

Grenzfall

fallende Gerade

Mitte x(A), x(B)

g(x)=

grenzgerade(x)=

Ha 2011

x^3=p x + q

f(x) = x^(3)
p = 0.4 (slider from -4 to 4, step 0.1)
q = 0.2 (slider from -1 to 1, step 0.01)
g(x) = p * x + q
h(x) = 0.5 * x - 0.1
r(x) = -2 * x - 0.25
qvonp: 2 / 3 * sqrt(p^(3) / 3)
gq(x) = p * x + qvonp
gq2(x) = p * x - qvonp
A, B = Intersect(gq, f)
poly(x) = x^(3) - g(x)
a: 2 * (qvonp / 2)^(1 / 3)
b = OrthogonalLine(B, xAxis)
c = OrthogonalLine(A, xAxis)
C: (a / 2, 0)
D, E, F = Root(poly)
d = OrthogonalLine(D, xAxis)
e = OrthogonalLine(F, xAxis)
i = OrthogonalLine(E, xAxis)
G, H, I = Intersect(f, g)
J = Intersect(g, gq2, 1)
j = Segment(D, G)
k = Segment(H, E)
l = Segment(I, F)
m = false
n = false
o = false
Text3: gq + ""
Text1: g + ""