Einführung in die Affenkästen
Author: Prof. Dr. Dörte Haftendorn

Kastenerweiterung

Kastenvermutung

Kasten unten

Tangenten

Hauptkasten

Erweiterung

f(x)=a x (x²-3 r²)

a = 0.1
r = -2
f(x) = a * x * (x^(2.0) - 3.0 * r^(2.0))
P, Q = Extremum(f)
O = (0, 0)
b = Line(Q, xAxis)
c = Line(P, xAxis)
B, C = Intersect(f, b)
D, E = Intersect(f, c)
F = Intersect(f, c, 2.0)
d = Line(F, yAxis)
e = Line(D, yAxis)
g = Line(B, yAxis)
h = Line(C, yAxis)
G = Intersect(g, c)
H = Intersect(c, h)
I = Intersect(c, yAxis)
J = Intersect(b, d)
K = Intersect(b, yAxis)
L = Intersect(b, e)
Vieleck1, b_1, j, f_1, g_1 = Polygon(B, J, F, G)
i = Segment(D, L)
k = Segment(I, K)
l = Segment(H, C)
m = Tangent(B, f)
n = Tangent(O, f)
A = Intersect(n, m)
p = Line(A, xAxis)
M = Intersect(p, g)
N = Intersect(p, d)
R = Intersect(p, h)
S = Intersect(p, yAxis)
T = Intersect(p, e)
q = Segment(T, P)
s = Segment(S, I)
t = Segment(R, H)
Vieleck2, m_1, g_2, e_1, n_1 = Polygon(M, G, E, N)
M' = Mirror(M, xAxis)
G' = Mirror(G, xAxis)
E' = Mirror(E, xAxis)
N' = Mirror(N, xAxis)
Vieleck2', m', g', e', n' = Polygon(M', G', E', N')
T' = Mirror(T, xAxis)
P' = Mirror(P, xAxis)
q' = Segment(T', P')
c_1 = Mirror(xAxis, s)
d_1 = Mirror(xAxis, t)
h_1 = Mirror(xAxis, s)
U = Intersect(b, yAxis)
Z = Intersect(n', yAxis)
A_1 = Intersect(h, n')
a_1 = Segment(Q, A_1)
V = Midpoint(M, A)
o = false
u = false
v = false
w = false
Vieleck3, p_1, i_1, o_1, j_1 = Polygon(P, (x(P), 0.0), O, (0.0, y(P)))
z = false
k_1 = false