Inversion

Konstr. als Cissoide

Original Konstr.

θ

θ

r(x)=\frac{a}{\cos(x)}-a \tan(x)

a = 2
r(x) = a / cos(x) - (a * tan(x))
θ = 0 (slider from 0 to 6.28, step 0.1)
K: (θ, r(θ))
P: (r(θ); θ)
Ortslinie1 = Locus(P, θ)
c: (x - a)^(2) + y^(2) = a^(2)
b: x = a
Q_1 = Point(c)
O = (0, 0)
d = Line(O, Q_1)
E = Intersect(b, d)
u = Vector(Q_1, E)
P'_1 = Translate(O, u)
v = Vector(O, P'_1)
Ortslinie2 = Locus(P'_1, Q_1)
e = Segment(O, P)
P_n = Mirror(P, O)
f = Segment(O, P_n)
K': (θ, 0)
g = Segment(K', K)
Q = Point(i)
A: (a, 0)
k = Circle(Q, A)
j = Line(O, Q)
P', P'' = Intersect(k, j)
Ortslinie3 = Locus(P', Q)
Ortslinie4 = Locus(P'', Q)
p: x^(2) + y^(2) = a^(2)
P_i = Mirror(P, p)
inv(x) = (a * cos(x) / (1 - sin(x)))
l = false
m = false
n = false
cis(x) = a / cos(x) - ((2 * a) * cos(x))
o = CurveCartesian((r(t) * cos(t)), (r(t) * sin(t)), t, 0, θ)
α = Angle(A, O, P)
β = Angle(A, O, P_n)