r(x)

K=(θ, r(θ))

θ

r(θ)

P=(r(θ); θ)

r(θ)

θ

P_n=(|r(θ)|;θ)

θ

r(x)=c\, e^{a\, x}

r(θ)=c\,e^{a\,θ}

https://www.geogebra.org/haftendorn
Haftendorn, Buch (Springer):
Kurven erkunden und verstehen
Kap 8.1.2: S. 223
www.kurven-erkunden-und-verstehen.de

Ha 2016

c = 1 (slider from -5 to 5, step 0.01)
a = 0.5 (slider from -5 to 5, step 0.01)
r(x) = (c * ℯ^((a * x)))
θ = 2.35 (slider from -5 to 5, step 0.05)
K: (θ, r(θ))
T: (x(K), 0)
O: (0, 0)
b = Segment(K, T)
P: (r(θ); θ)
d = Segment(P, O)
A = Point(xAxis)
α = Angle(A, O, P)
P_n = Mirror(P, O)
β = Angle(A, O, P_n)
e = Segment(O, P_n)
anf = -4.65
end: 5
f = CurveCartesian((r(t) * cos(t)), (r(t) * sin(t)), t, anf, end)
g = false