Auteur : Reinhard Weiß

O = Intersect(xAxis, yAxis)
Z = (-0.17058529815619147, 0.25965647166873074)
u = Vector(O, Z)
r = 1.2 (slider from 1 to 2, step 0.1)
c = Circle(Z, r)
Z' = Point(c)
Z'': (0.5 * (Z' + 1 / Z'))
Ortslinie1 = Locus(Z'', Z')
A = Point(yAxis)
a = OrthogonalLine(A, yAxis)
B = Point(a)
C = Point(a)
b = Ray(A, C)
d = Ray(A, B)
D = Point(d)
E = Point(b)
D_1: D - sqrt(D^(2) - 1)
D_2: (D_1 * r)
α = 3.036872898470133 rad (slider from 0 to 360°, step °)
D_3 = Rotate(D_2, α)
D_4: D_3 + u
D': (0.5 * (D_4 + 1 / D_4))
Ortslinie2 = Locus(D', D)
E_1: E + sqrt(E^(2) - 1)
E_2: (r * E_1)
E_3 = Rotate(E_2, α)
E_4: E_3 + u
E': (0.5 * (E_4 + 1 / E_4))
Ortslinie3 = Locus(E', E)
e = Circle(O, A)
F = Intersect(e, yAxis, 2)
G = Midpoint(A, O)
H = Midpoint(F, O)
f = OrthogonalLine(G, yAxis)
g, h = Strahlen(G)
i, j = Strahlen(O)
k, l = Strahlen(H)
m, n = Strahlen(F)
I = Point(h)
J = Point(j)
K = Point(l)
L = Point(n)
z_1 = Minus(α, r, u, I)
z_2 = Minus(α, r, u, J)
z_3 = Minus(α, r, u, K)
z_4 = Minus(α, r, u, L)
Ortslinie4 = Locus(z_1, I)
Ortslinie5 = Locus(z_2, J)
Ortslinie6 = Locus(z_3, K)
Ortslinie7 = Locus(z_4, L)
M = Point(g)
N = Point(i)
P = Point(k)
Q = Point(m)
z_5 = Plus(α, r, u, M)
z_6 = Plus(α, r, u, N)
z_7 = Plus(α, r, u, P)
z_8 = Plus(α, r, u, Q)
Ortslinie8 = Locus(z_5, M)
Ortslinie9 = Locus(z_6, N)
Ortslinie10 = Locus(z_7, P)
Ortslinie11 = Locus(z_8, Q)
R = Midpoint(A, G)
U = Midpoint(H, F)
p, q = Strahlen(R)
c_1, d_1 = Strahlen(U)
V = Point(q)
B_1 = Point(d_1)
z_{9} = Minus(α, r, u, V)
z_{12} = Minus(α, r, u, B_1)
Ortslinie12 = Locus(z_{9}, V)
Ortslinie15 = Locus(z_{12}, B_1)
C_1 = Point(p)
H_1 = Point(c_1)
z_{13} = Plus(α, r, u, C_1)
z_{16} = Plus(α, r, u, H_1)
Ortslinie16 = Locus(z_{13}, C_1)
Ortslinie19 = Locus(z_{16}, H_1)
I_1 = Point(Ortslinie16)
J_1 = Point(Ortslinie16)
K_1 = Point(yAxis)
L_1 = Point(yAxis)
f_1 = Segment(K_1, L_1)
e_1 = Segment((-1, 0), (1, 0))
S = Midpoint(H, O)
T = Midpoint(O, G)
s, t = Strahlen(S)
a_1, b_1 = Strahlen(T)
W = Point(t)
A_1 = Point(b_1)
F_1 = Point(s)
G_1 = Point(a_1)
z_{10} = Minus(α, r, u, W)
z_{11} = Minus(α, r, u, A_1)
z_{14} = Plus(α, r, u, F_1)
z_{15} = Plus(α, r, u, G_1)
Ortslinie13 = Locus(z_{10}, W)
Ortslinie14 = Locus(z_{11}, A_1)
Ortslinie17 = Locus(z_{14}, F_1)
Ortslinie18 = Locus(z_{15}, G_1)

Tool: Strahlen
Strahlen[ <Punkt> ]
Input: A
Output: b, d

a = OrthogonalLine(A, yAxis)
B = Point(a)
C = Point(a)
b = Ray(A, C)
d = Ray(A, B)

Tool: Minus-Arm (command Minus)
Input: α, r, u, D
Output: D'

D_1: D - sqrt(D^(2) - 1)
D_2: (D_1 * r)
D_3 = Rotate(D_2, α)
D_4: D_3 + u
D': (0.5 * (D_4 + 1 / D_4))

Tool: Plus-Arm (command Plus)
Input: α, r, u, E
Output: E'

E_1: E + sqrt(E^(2) - 1)
E_2: (r * E_1)
E_3 = Rotate(E_2, α)
E_4: E_3 + u
E': (0.5 * (E_4 + 1 / E_4))