Poincare-Kreis-Modell Quadrate
Author: Prof. Dr. Dörte Haftendorn
Date: 27 Juni 2013

Kreis

Euklidische Geraden

Wo sind 4 kongruente Quadrate?
Erzeuge ein 5. dazu.

Sind die Innenwinkel der Quadrate gleich groß? 

Wo sind kongruente Dreiecke?

Hyperbolische Geometrie

Ha 2013

Symmetrieachsen

C = (-1.18, 1.1)
D = (-1.06, -0.76)
a = LineBisector(C, D)
D' = Mirror(D, c)
i = LineBisector(D, D')
H = Intersect(a, i)
k = Circle(H, D)
I, J = Intersect(c, k)
p = CircumcircleArc(I, D, J)
b = Tangent(C, p)
w = 3.6322511575784526 rad
A, B = Intersect(c, b)
O = (0, 0)
d = Line(C, O)
b' = Mirror(b, d)
I' = Mirror(I, d)
D'_1 = Mirror(D, d)
J' = Mirror(J, d)
p' = CircumcircleArc(I', D'_1, J')
e = OrthogonalLine(O, d)
E = Intersect(p', e)
D'_2 = Mirror(D, d)
E' = Mirror(E, O)
C' = Mirror(C, O)
F = (1.6, 6.12)
f, G, K, L = hypger(E, C', c)
g, M, N, P = hypger(E', C', c)
h = Circle(O, C)
j = false
I'_1 = Mirror(I, f)
J'_1 = Mirror(J, f)
l = false
I'_2 = Mirror(I, f)
D'_3 = Mirror(D, f)
J'_2 = Mirror(J, f)
p'_1 = CircumcircleArc(I'_2, D'_3, J'_2)
E'' = Mirror(E', f)
C'_1 = Mirror(C, f)
E''_1 = Mirror(E', p')
C'' = Mirror(C', p')
E'_1 = Mirror(E, p)
C''_1 = Mirror(C', p)
q, Q, R, S = hypger(E'_1, C''_1, c)
r, T, U, V = hypger(E'_1, C, c)
s, W, Z, A_1 = hypger(C''_1, E', c)
t, B_1, C_1, D_1 = hypger(C'_1, E, c)
c_1, E_1, F_1, G_1 = hypger(E''_1, C'', c)
d_1, H_1, I_1, J_1 = hypger(E''_1, C, c)
e_1, K_1, L_1, M_1 = hypger(C'', E, c)
f_1, N_1, O_1, P_1 = hypger(E'', C', c)
g_1, Q_1, R_1, S_1 = hypger(C'_1, E, c)
m = false

Tool: hypger
Punkt, Punkt, Hyp-Kreis  ergibt Geradenbogen
Input: C, D, c
Output: p, J, I, H

a = LineBisector(C, D)
D' = Mirror(D, c)
i = LineBisector(D, D')
H = Intersect(a, i)
k = Circle(H, D)
I, J = Intersect(c, k)
p = CircumcircleArc(I, D, J)