Winkeldreiteilungs-Versuch Karel M.
Author: Karel M., D.Haftendorn
Date: Mai 06

Trigon-Verlag, Potsdam

Ha 06

Nach K.M. 2005 Trigon-Verlag

Variante A_1,B_1

α = 0.785398163397449 rad
A = Point(yAxis)
O = Intersect(xAxis, yAxis)
B = Rotate(A, α, O)
β = Angle(A, O, B)
C = Rotate(A, -α, O)
γ = Angle(C, O, A)
c = Circle(O, A)
a = Segment(B, C)
D: (x(B) / 3, y(B))
E: (x(C) / 3, y(C))
H: (0, y(C))
d = Circle(O, H)
b = Line(D, yAxis)
e = Line(E, yAxis)
f = Line(B, b)
g = Line(C, e)
dritsek: 2 x(C) / 3
F, G = Intersect(c, b)
I, J = Intersect(c, e)
K, L = Intersect(d, b)
M, N = Intersect(d, e)
h = Circle(M, K)
k = Circle(I, F)
P, Q = Intersect(h, d)
R, S = Intersect(k, c)
i = Ray(O, B)
j = Ray(O, C)
l = Line(R, P)
T = Intersect(l, j)
p = CircleArc(M, K, P)
q = CircleArc(I, F, R)
r = Circle(O, T)
U, V = Intersect(r, b)
W, Y = Intersect(r, e)
δ = Angle(T, O, W)
ε = Angle(W, O, U)
ζ = Angle(U, O, B)
T1: "δ = " + δ
T2: "ε = " + ε
T3: "ζ = " + ζ
n = Segment(F, I)
s = Segment(I, R)
m = Segment(U, W)
t = Segment(W, T)
a_1 = Segment(K, M)
b_1 = Segment(M, P)
T4: "m = " + m
T5: "t = " + t
T6: "φ = " + (α + β)
T7: "φ/3 = " + (2 α / 3)
Z = Mirror(R, yAxis)
c_1 = Line(Z, yAxis)
A_1 = Intersect(i, c_1)
d_1 = Circle(O, A_1)
B_1, C_1 = Intersect(d_1, b)
e_1 = CircleArc(O, B_1, A_1)
η = Angle(B_1, O, A_1)
T11: "η = " + η