r

a r

θ

Fußpunktkurve

r(\theta)=e^{a\, \theta}

https://www.geogebra.org/haftendorn
Haftendorn, Buch (Springer):
Kurven erkunden und verstehen
Kap 8.1.2.4: S. 228
www.kurven-erkunden-und-verstehen.de

Ha 2016

θ = 4 (slider from -5 to 7, step 0.1)
a = 0.4 (slider from -5 to 5, step 0.1)
r(x) = ℯ^((a * x))
K: (θ, r(θ))
P: (r(θ); θ)
Ortslinie1 = Locus(P, θ)
O = (0, 0)
b = Segment(O, P)
c = OrthogonalLine(O, b)
d = Circle(O, (a * b))
B, N = Intersect(d, c)
e = Segment(N, P)
f = OrthogonalLine(P, e)
D = Point(f)
α = Angle(D, P, N)
β = Angle(P, O, N)
g = Segment(O, N)
K': (θ, 0)
H_K: (θ, (a * r(θ)))
h = Segment(K, K')
i = Segment(H_K, K')
k = Circle(N, P)
j = OrthogonalLine(O, f)
F = Intersect(f, j)
γ = Angle(P, F, O)
Ortslinie2 = Locus(F, θ)
l = true
m = false