β

β

https://www.geogebra.org/haftendorn
Haftendorn, Buch (Springer):
Kurven erkunden und verstehen
Kap 8.1.2: S. 225
www.kurven-erkunden-und-verstehen.de

Ha 2016

O: (0, 0)
a = -0.2
c: 1
r(x) = (c * exp((a * x)))
b = CurveCartesian((r(t) * cos(t)), (r(t) * sin(t)), t, -8.26, 10)
A = Point(b)
d = Segment(O, A)
g = Circle(O, ((-a) * d))
e = OrthogonalLine(O, d)
B, C = Intersect(g, e)
h = Ray(B, A)
i = OrthogonalLine(A, h)
D = Point(i)
j = Ray(A, D)
S = Point(j)
P = Point(j)
t_A: (247 / 180 * π)
f = Circle(O, (a * d))
E = Point(xAxis)
Q = Point(i)
k = Line(Q, d)
G = Point(k)
l = Ray(Q, G)
m: y = d
H = Intersect(r, m, (-8.255537625417142, 5.21274988259811))
n = Line(H, yAxis)
J = (-10.5, -4.08)
I = (-10.56, -2.1)
ll: l
K = Point(b)
p = Segment(O, K)
q = OrthogonalLine(O, p)
s = Circle(O, ((-a) * p))
L, M = Intersect(s, q)
t = Segment(L, K)
a_1 = OrthogonalLine(K, t)
N = Point(a_1)
b_1 = Segment(K, N)
u = Vector(S, P)
J' = Translate(J, u)
I' = Translate(I, u)
J'' = Translate(J', u)
I'' = Translate(I', u)
J''' = Translate(J'', u)
I''' = Translate(I'', u)
Q_1 = Translate(J''', u)
R = Translate(I''', u)
Bild1' = Translate(Bild1, u)
J''_1 = Translate(J', u)
Bild1'' = Translate(Bild1', u)
Bild1''' = Translate(Bild1'', u)
T = (6.419753066416765, -5.747581890538987)
U = (-1.08, -4.36)
V = (0.1, -5.98)
W = (1.36, -3.52)
Z = (3.32, -4.22)
A_1 = (2.88, -1.86)
B_1 = (4.76, -0.98)
C_1 = (2.7, 0.28)
D_1 = (3.68, 2.2)
β = Angle(A, Q, G)
E_1 = Point(a_1)
α = Angle(E_1, K, O)
F_1 = Point(b)
O' = Rotate(O, (-β), F_1)
γ = Angle(O', F_1, O)
c_1 = Segment(O, F_1)
G_1 = Point(b)
H_1 = (0.02, 2.18)
I_1 = (-2.06, 2.82)
o = false