Experimentieren mit Symmetrieachsen
Author: Mag. G.Wengler

Hier kannst du doppelt symmetrische Figuren manipulieren. Erforsche, wie die Achsen zueinander stehen.

1.Achse

2.Achse

Symmetrie-Spiel

gespiegelte Achse

Die dunkelblaue Figur kannst du verändern!

Was passiert, wenn du die Punkte A und B bewegst?

A_4 = (-4.552754607177498, 2.5108787584869043)
B_4 = (-3.4164578079534436, 2.2691134820562544)
C = (-3.6582230843840935, 3.2119980601357896)
D = (-3.0230397672162947, 3.8208069835111527)
E = (-3.4889873908826377, 4.638413191076625)
F = (-4.528578079534434, 3.961470417070805)
G = (-5.089033947623667, 3.6669563530552836)
Vieleck1, a, b, c, d, e, f, g = Polygon(A_4, B_4, C, D, E, F, G)
A = (0.9111406401551904, -0.3177749757516993)
h = OrthogonalLine(A, xAxis)
i = OrthogonalLine(A, h)
A'_1 = Mirror(A_4, h)
B'_1 = Mirror(B_4, h)
C'_1 = Mirror(C, h)
D'_1 = Mirror(D, h)
E'_1 = Mirror(E, h)
F'_1 = Mirror(F, h)
G'_1 = Mirror(G, h)
Vieleck1'_1, a'_1, b'_1, c'_1, d'_1, e'_1, f'_1, g'_1 = Polygon(A'_1, B'_1, C'_1, D'_1, E'_1, F'_1, G'_1)
A''_1 = Rotate(A'_1, 270*°, A)
B''_1 = Rotate(B'_1, 270*°, A)
C''_1 = Rotate(C'_1, 270*°, A)
D''_1 = Rotate(D'_1, 270*°, A)
E''_1 = Rotate(E'_1, 270*°, A)
F''_1 = Rotate(F'_1, 270*°, A)
G''_1 = Rotate(G'_1, 270*°, A)
A'''_1 = Mirror(A''_1, h)
B'''_1 = Mirror(B''_1, h)
C'''_1 = Mirror(C''_1, h)
D'''_1 = Mirror(D''_1, h)
E'''_1 = Mirror(E''_1, h)
F'''_1 = Mirror(F''_1, h)
G'''_1 = Mirror(G''_1, h)
B = (2.41008535402522, 2.7284675072744897)
j_3 = OrthogonalLine(B, i)
k_2 = OrthogonalLine(B, h)
A' = Mirror(A_4, j_3)
B' = Mirror(B_4, j_3)
C' = Mirror(C, j_3)
D' = Mirror(D, j_3)
E' = Mirror(E, j_3)
F' = Mirror(F, j_3)
G' = Mirror(G, j_3)
Vieleck1', a', b', c', d', e', f', g' = Polygon(A', B', C', D', E', F', G')
J = Mirror(A'_1, j_3)
K = Mirror(B'_1, j_3)
L = Mirror(C'_1, j_3)
M = Mirror(D'_1, j_3)
N = Mirror(E'_1, j_3)
O = Mirror(F'_1, j_3)
P = Mirror(G'_1, j_3)
Vieleck2, j_2, k, l, m, n, o, p = Polygon(J, K, L, M, N, O, P)
A'''_2 = Mirror(A''_1, j_3)
B'''_2 = Mirror(B''_1, j_3)
C'''_2 = Mirror(C''_1, j_3)
D'''_2 = Mirror(D''_1, j_3)
E'''_2 = Mirror(E''_1, j_3)
F'''_2 = Mirror(F''_1, j_3)
G'''_2 = Mirror(G''_1, j_3)
Q = Mirror(A'''_1, j_3)
R = Mirror(B'''_1, j_3)
S = Mirror(C'''_1, j_3)
T = Mirror(D'''_1, j_3)
U = Mirror(E'''_1, j_3)
V = Mirror(F'''_1, j_3)
W = Mirror(G'''_1, j_3)
H' = Mirror(A, j_3)
A'' = Rotate(A', 270*°, B)
B'' = Rotate(B', 270*°, B)
C'' = Rotate(C', 270*°, B)
D'' = Rotate(D', 270*°, B)
E'' = Rotate(E', 270*°, B)
F'' = Rotate(F', 270*°, B)
G'' = Rotate(G', 270*°, B)
J' = Rotate(J, 270*°, B)
K' = Rotate(K, 270*°, B)
L' = Rotate(L, 270*°, B)
M' = Rotate(M, 270*°, B)
N' = Rotate(N, 270*°, B)
O' = Rotate(O, 270*°, B)
P' = Rotate(P, 270*°, B)
Z = Rotate(A'''_2, 270*°, B)
A_1 = Rotate(B'''_2, 270*°, B)
B_1 = Rotate(C'''_2, 270*°, B)
C_1 = Rotate(D'''_2, 270*°, B)
D_1 = Rotate(E'''_2, 270*°, B)
E_1 = Rotate(F'''_2, 270*°, B)
F_1 = Rotate(G'''_2, 270*°, B)
Q' = Rotate(Q, 270*°, B)
R' = Rotate(R, 270*°, B)
S' = Rotate(S, 270*°, B)
T' = Rotate(T, 270*°, B)
U' = Rotate(U, 270*°, B)
V' = Rotate(V, 270*°, B)
W' = Rotate(W, 270*°, B)
A''' = Mirror(A'', j_3)
B''' = Mirror(B'', j_3)
C''' = Mirror(C'', j_3)
D''' = Mirror(D'', j_3)
E''' = Mirror(E'', j_3)
F''' = Mirror(F'', j_3)
G''' = Mirror(G'', j_3)
J'' = Mirror(J', j_3)
K'' = Mirror(K', j_3)
L'' = Mirror(L', j_3)
M'' = Mirror(M', j_3)
N'' = Mirror(N', j_3)
O'' = Mirror(O', j_3)
P'' = Mirror(P', j_3)
Z' = Mirror(Z, j_3)
G_1 = Mirror(A_1, j_3)
H_1 = Mirror(B_1, j_3)
I_1 = Mirror(C_1, j_3)
J_1 = Mirror(D_1, j_3)
K_1 = Mirror(E_1, j_3)
L_1 = Mirror(F_1, j_3)
Q'' = Mirror(Q', j_3)
R'' = Mirror(R', j_3)
S'' = Mirror(S', j_3)
T'' = Mirror(T', j_3)
U'' = Mirror(U', j_3)
V'' = Mirror(V', j_3)
W'' = Mirror(W', j_3)
j = OrthogonalLine(H', i)
M_1 = Mirror(A'_1, i)
N_1 = Mirror(B'_1, i)
O_1 = Mirror(C'_1, i)
P_1 = Mirror(D'_1, i)
Q_1 = Mirror(E'_1, i)
R_1 = Mirror(F'_1, i)
S_1 = Mirror(G'_1, i)
Vieleck3, m_1, n_1, o_1, p_1, q_1, r_1, s_1 = Polygon(M_1, N_1, O_1, P_1, Q_1, R_1, S_1)
J'_1 = Mirror(J, i)
K'_1 = Mirror(K, i)
L'_1 = Mirror(L, i)
M'_1 = Mirror(M, i)
N'_1 = Mirror(N, i)
O'_1 = Mirror(O, i)
P'_1 = Mirror(P, i)
Vieleck2', j'_1, k'_1, l'_1, m'_1, n'_1, o'_1, p'_1 = Polygon(J'_1, K'_1, L'_1, M'_1, N'_1, O'_1, P'_1)
A''_2 = Mirror(A', i)
B''_2 = Mirror(B', i)
C''_2 = Mirror(C', i)
D''_2 = Mirror(D', i)
E''_2 = Mirror(E', i)
F''_2 = Mirror(F', i)
G''_2 = Mirror(G', i)
Vieleck1'', a''_2, b''_2, c''_2, d''_2, e''_2, f''_2, g''_2 = Polygon(A''_2, B''_2, C''_2, D''_2, E''_2, F''_2, G''_2)
A'_2 = Mirror(A_4, i)
B'_2 = Mirror(B_4, i)
C'_2 = Mirror(C, i)
D'_2 = Mirror(D, i)
E'_2 = Mirror(E, i)
F'_2 = Mirror(F, i)
G'_2 = Mirror(G, i)
Vieleck1'_2, a'_2, b'_2, c'_2, d'_2, e'_2, f'_2, g'_2 = Polygon(A'_2, B'_2, C'_2, D'_2, E'_2, F'_2, G'_2)
A'_3 = Mirror(A_4, k_2)
B'_3 = Mirror(B_4, k_2)
C'_3 = Mirror(C, k_2)
D'_3 = Mirror(D, k_2)
E'_3 = Mirror(E, k_2)
F'_3 = Mirror(F, k_2)
G'_3 = Mirror(G, k_2)
J'_2 = Mirror(J, k_2)
K'_2 = Mirror(K, k_2)
L'_2 = Mirror(L, k_2)
M'_2 = Mirror(M, k_2)
N'_2 = Mirror(N, k_2)
O'_2 = Mirror(O, k_2)
P'_2 = Mirror(P, k_2)
T_1 = Mirror(A'_1, k_2)
U_1 = Mirror(B'_1, k_2)
V_1 = Mirror(C'_1, k_2)
W_1 = Mirror(D'_1, k_2)
Z_1 = Mirror(E'_1, k_2)
A_2 = Mirror(F'_1, k_2)
B_2 = Mirror(G'_1, k_2)
A''_3 = Mirror(A', k_2)
B''_3 = Mirror(B', k_2)
C''_3 = Mirror(C', k_2)
D''_3 = Mirror(D', k_2)
E''_3 = Mirror(E', k_2)
F''_3 = Mirror(F', k_2)
G''_3 = Mirror(G', k_2)
q = Mirror(k_2, i)
A'_4 = Mirror(A_4, k_2)
B'_4 = Mirror(B_4, k_2)
C'_4 = Mirror(C, k_2)
D'_4 = Mirror(D, k_2)
E'_4 = Mirror(E, k_2)
F'_4 = Mirror(F, k_2)
G'_4 = Mirror(G, k_2)
Vieleck1'_3, a'_4, b'_4, c'_4, d'_4, e'_4, f'_4, g'_4 = Polygon(A'_4, B'_4, C'_4, D'_4, E'_4, F'_4, G'_4)
C_2 = Mirror(A'_2, q)
D_2 = Mirror(B'_2, q)
E_2 = Mirror(C'_2, q)
F_2 = Mirror(D'_2, q)
G_2 = Mirror(E'_2, q)
H_2 = Mirror(F'_2, q)
I_2 = Mirror(G'_2, q)
Vieleck4, c_2, d_2, e_2, f_2, g_2, h_2, i_2 = Polygon(C_2, D_2, E_2, F_2, G_2, H_2, I_2)
J'_3 = Mirror(J, k_2)
K'_3 = Mirror(K, k_2)
L'_3 = Mirror(L, k_2)
M'_3 = Mirror(M, k_2)
N'_3 = Mirror(N, k_2)
O'_3 = Mirror(O, k_2)
P'_3 = Mirror(P, k_2)
Vieleck2'_1, j'_3, k'_3, l'_3, m'_3, n'_3, o'_3, p'_3 = Polygon(J'_3, K'_3, L'_3, M'_3, N'_3, O'_3, P'_3)
J_2 = Mirror(J'_3, i)
K_2 = Mirror(K'_3, i)
L_2 = Mirror(L'_3, i)
M_2 = Mirror(M'_3, i)
N_2 = Mirror(N'_3, i)
O_2 = Mirror(O'_3, i)
P_2 = Mirror(P'_3, i)
Vieleck5, j_1, k_1, l_2, m_2, n_2, o_2, p_2 = Polygon(J_2, K_2, L_2, M_2, N_2, O_2, P_2)
Q_2 = Mirror(A'_1, k_2)
R_2 = Mirror(B'_1, k_2)
S_2 = Mirror(C'_1, k_2)
T_2 = Mirror(D'_1, k_2)
U_2 = Mirror(E'_1, k_2)
V_2 = Mirror(F'_1, k_2)
W_2 = Mirror(G'_1, k_2)
Vieleck6, q_2, r_2, s_2, t_2, u_2, v_2, w_2 = Polygon(Q_2, R_2, S_2, T_2, U_2, V_2, W_2)
Z_2 = Mirror(Q_2, i)
A_3 = Mirror(R_2, i)
B_3 = Mirror(S_2, i)
C_3 = Mirror(T_2, i)
D_3 = Mirror(U_2, i)
E_3 = Mirror(V_2, i)
F_3 = Mirror(W_2, i)
Vieleck6', z_2, a_3, b_3, c_3, d_3, e_3, f_3 = Polygon(Z_2, A_3, B_3, C_3, D_3, E_3, F_3)
A''_4 = Mirror(A', k_2)
B''_4 = Mirror(B', k_2)
C''_4 = Mirror(C', k_2)
D''_4 = Mirror(D', k_2)
E''_4 = Mirror(E', k_2)
F''_4 = Mirror(F', k_2)
G''_4 = Mirror(G', k_2)
Vieleck1''_1, a''_4, b''_4, c''_4, d''_4, e''_4, f''_4, g''_4 = Polygon(A''_4, B''_4, C''_4, D''_4, E''_4, F''_4, G''_4)
G_3 = Mirror(A''_4, i)
H_3 = Mirror(B''_4, i)
I_3 = Mirror(C''_4, i)
J_3 = Mirror(D''_4, i)
K_3 = Mirror(E''_4, i)
L_3 = Mirror(F''_4, i)
M_3 = Mirror(G''_4, i)
Vieleck7, g_3, h_3, i_3, j_4, k_3, l_3, m_3 = Polygon(G_3, H_3, I_3, J_3, K_3, L_3, M_3)