SSS - Konstruktion
Author: Anita Dorfmayr und Walter Klinger
Date: 2.10.2005

Öffne das dynamische Arbeitsblatt und schaue dir die Konstruktion an. Schreibe mit eigenen Worten ein Konstruktionsprotokoll auf.

Versuche selbst, ein Dreieck zu konstruieren, von dem drei Seiten gegeben sind.

127

278

128

178

157

248

136

146

346

134

135

246

389

238

289

239

359

268

479

469

467

679

579

468

129

237

367

169

189

378

347

149

3

4

5

2

7

6

8

9

1

lista2: {127.0, 128.0, 129.0, 134.0, 135.0, 136.0, 146.0, 149.0, 157.0, 169.0, 178.0, 189.0, 237.0, 238.0, 239.0, 246.0, 248.0, 268.0, 278.0, 289.0, 346.0, 347.0, 359.0, 367.0, 378.0, 389.0, 467.0, 468.0, 469.0, 479.0, 579.0, 679.0}
A1 = 127
x1 = 0 (slider from 0 to 10, step 5)
x2 = 5 (slider from 0 to 10, step 5)
x3 = 0 (slider from 0 to 10, step 5)
y1 = -5 (slider from -5 to 5, step 5)
y2 = -5 (slider from -5 to 5, step 5)
y3 = 5 (slider from -5 to 5, step 5)
D = (0, 5)
E = (5, 5)
F = (10, 5)
G = (10, 0)
H = (5, 0)
I = (0, 0)
J = (5, -5)
K = (10, -5)
L = (0, -5)
A: (x1, y1)
B: (x2, y2)
C: (x3, y3)
a = Segment(A, B)
b = Segment(A, C)
c = Segment(B, C)
lista1: {Polygon[A, B, C]}
M = (12, 4)
N = (13, 4)
polígono1, m, n, d, e, O, P = Polygon(M, N, 4.0)
Q = (13.5, 4)
R = (14.5, 4)
polígono2, q, r, f, g, S, T = Polygon(Q, R, 4.0)
U = (15, 4)
V = (16, 4)
polígono3, u, v, h, i, W, Z = Polygon(U, V, 4.0)
A_1 = (16.5, 4)
B_1 = (17.5, 4)
polígono4, a_1, b_1, j, k, C_1, D_1 = Polygon(A_1, B_1, 4.0)
E_1 = (18, 4)
F_1 = (19, 4)
polígono5, e_1, f_1, l, p, G_1, H_1 = Polygon(E_1, F_1, 4.0)
I_1 = (19.5, 4)
J_1 = (20.5, 4)
polígono6, i_1, j_1, s, t, K_1, L_1 = Polygon(I_1, J_1, 4.0)
A2 = NaN
A3 = NaN
A4 = NaN
A5 = NaN
A6 = NaN
A7 = NaN
A8 = NaN
A9 = NaN
A10 = NaN
A11 = NaN
A12 = NaN
A13 = NaN
A14 = NaN
A15 = NaN
A16 = NaN
A17 = NaN
A18 = NaN
A19 = NaN
A20 = NaN
A21 = NaN
A22 = NaN
A23 = NaN
A24 = NaN
A25 = NaN
A26 = NaN
A27 = NaN
A28 = NaN
A29 = NaN
A30 = NaN
A31 = NaN
A32 = NaN
M_1 = (12, 1.5)
N_1 = (13, 1.5)
polígono7, m_1, n_1, c_1, d_1, O_1, P_1 = Polygon(M_1, N_1, 4.0)
Q_1 = (13.5, 1.5)
R_1 = (14.5, 1.5)
polígono8, q_1, r_1, g_1, h_1, S_1, T_1 = Polygon(Q_1, R_1, 4.0)
U_1 = (15, 1.5)
V_1 = (16, 1.5)
polígono9, u_1, v_1, k_1, l_1, W_1, Z_1 = Polygon(U_1, V_1, 4.0)
A_2 = (16.5, 1.5)
B_2 = (17.5, 1.5)
polígono10, a_2, b_2, p_1, s_1, C_2, D_2 = Polygon(A_2, B_2, 4.0)
E_2 = (18, 1.5)
F_2 = (19, 1.5)
polígono11, e_2, f_2, t_1, c_2, G_2, H_2 = Polygon(E_2, F_2, 4.0)
I_2 = (19.5, 1.5)
J_2 = (20.5, 1.5)
polígono12, i_2, j_2, d_2, g_2, K_2, L_2 = Polygon(I_2, J_2, 4.0)
M_2 = (12, -1)
N_2 = (13, -1)
polígono13, m_2, n_2, h_2, k_2, O_2, P_2 = Polygon(M_2, N_2, 4.0)
Q_2 = (13.5, -1)
R_2 = (14.5, -1)
polígono14, q_2, r_2, l_2, p_2, S_2, T_2 = Polygon(Q_2, R_2, 4.0)
U_2 = (15, -1)
V_2 = (16, -1)
polígono15, u_2, v_2, s_2, t_2, W_2, Z_2 = Polygon(U_2, V_2, 4.0)
A_3 = (16.5, -1)
B_3 = (17.5, -1)
polígono16, a_3, b_3, c_3, d_3, C_3, D_3 = Polygon(A_3, B_3, 4.0)
E_3 = (18, -1)
F_3 = (19, -1)
polígono17, e_3, f_3, g_3, h_3, G_3, H_3 = Polygon(E_3, F_3, 4.0)
I_3 = (19.5, -1)
J_3 = (20.5, -1)
polígono18, i_3, j_3, k_3, l_3, K_3, L_3 = Polygon(I_3, J_3, 4.0)
M_3 = (12, -3.5)
N_3 = (13, -3.5)
polígono19, m_3, n_3, p_3, q_3, O_3, P_3 = Polygon(M_3, N_3, 4.0)
Q_3 = (13.5, -3.5)
R_3 = (14.5, -3.5)
polígono20, q_4, r_3, s_3, t_3, S_3, T_3 = Polygon(Q_3, R_3, 4.0)
U_3 = (15, -3.5)
V_3 = (16, -3.5)
polígono21, u_3, v_3, a_4, b_4, W_3, Z_3 = Polygon(U_3, V_3, 4.0)
A_4 = (16.5, -3.5)
B_4 = (17.5, -3.5)
polígono22, a_5, b_5, c_4, d_4, C_4, D_4 = Polygon(A_4, B_4, 4.0)
E_4 = (18, -3.5)
F_4 = (19, -3.5)
polígono23, e_4, f_4, g_4, h_4, G_4, H_4 = Polygon(E_4, F_4, 4.0)
I_4 = (19.5, -3.5)
J_4 = (20.5, -3.5)
polígono24, i_4, j_4, k_4, l_4, K_4, L_4 = Polygon(I_4, J_4, 4.0)
M_4 = (9, -7.5)
N_4 = (10, -7.5)
polígono25, m_4, n_4, p_4, r_4, O_4, P_4 = Polygon(M_4, N_4, 4.0)
Q_4 = (10.5, -7.5)
R_4 = (11.5, -7.5)
polígono26, q_5, r_5, s_4, t_4, S_4, T_4 = Polygon(Q_4, R_4, 4.0)
U_4 = (12, -7.5)
V_4 = (13, -7.5)
polígono27, u_4, v_4, c_5, d_5, W_4, Z_4 = Polygon(U_4, V_4, 4.0)
A_5 = (13.5, -7.5)
B_5 = (14.5, -7.5)
polígono28, a_6, b_6, e_5, f_5, C_5, D_5 = Polygon(A_5, B_5, 4.0)
E_5 = (15, -7.5)
F_5 = (16, -7.5)
polígono29, e_6, f_6, g_5, h_5, G_5, H_5 = Polygon(E_5, F_5, 4.0)
I_5 = (16.5, -7.5)
J_5 = (17.5, -7.5)
polígono30, i_5, j_5, k_5, l_5, K_5, L_5 = Polygon(I_5, J_5, 4.0)
M_5 = (18, -7.5)
N_5 = (19, -7.5)
polígono31, m_5, n_5, p_5, s_5, O_5, P_5 = Polygon(M_5, N_5, 4.0)
Q_5 = (19.5, -7.5)
R_5 = (20.5, -7.5)
polígono32, q_6, r_6, t_5, c_6, S_5, T_5 = Polygon(Q_5, R_5, 4.0)
U_5 = Midpoint(m)
V_5 = Midpoint(f)
W_5 = Midpoint(q)
Z_5 = Midpoint(h)
A_6 = Midpoint(u)
B_6 = Midpoint(j)
C_6 = Midpoint(H_1, F_1)
E_6 = Midpoint(H_2, F_2)
D_6 = Midpoint(t)
F_6 = Midpoint(n_1)
G_6 = Midpoint(h_1)
H_6 = Midpoint(l_1)
I_6 = Midpoint(v_1)
J_6 = Midpoint(r_1)
K_6 = Midpoint(s_1)
L_6 = Midpoint(g_2)
M_6 = Midpoint(i_2)
N_6 = Midpoint(j_2)
O_6 = Midpoint(h_2)
P_6 = Midpoint(l_2)
Q_6 = Midpoint(q_2)
R_6 = Midpoint(s_2)
S_6 = Midpoint(u_2)
T_6 = Midpoint(a_3)
U_6 = Midpoint(H_3, F_3)
V_6 = Midpoint(k_3)
W_6 = Midpoint(j_3)
Z_6 = Midpoint(i_3)
A_7 = Midpoint(s)
B_7 = Midpoint(i_1)
C_7 = Midpoint(l_4)
D_7 = Midpoint(k_4)
E_7 = Midpoint(j_4)
F_7 = Midpoint(q_3)
G_7 = Midpoint(t_3)
H_7 = Midpoint(r_3)
I_7 = Midpoint(b_4)
J_7 = Midpoint(v_3)
K_7 = Midpoint(b_5)
L_7 = Midpoint(H_4, F_4)
M_7 = Midpoint(m_4)
N_7 = Midpoint(q_5)
O_7 = Midpoint(v_4)
P_7 = Midpoint(b_6)
Q_7 = Midpoint(g_5)
R_7 = Midpoint(k_5)
S_7 = Midpoint(s_5)
T_7 = Midpoint(c_6)
polígono33, p_6, m_6, u_5 = Polygon(M, U_5, P)
polígono34, w_5, t_6, v_5 = Polygon(T, V_5, W_5)
polígono35, z_5, u_6, a_7 = Polygon(U, A_6, Z_5)
polígono36, b_7, a_8, d_6 = Polygon(A_1, D_1, B_6)
polígono37, e_7, h_6, c_7 = Polygon(H_1, C_6, E_1)
polígono38, d_7, b_8, a_9 = Polygon(B_7, A_7, D_6)
polígono39, f_7, m_7, n_6 = Polygon(M_1, N_1, F_6)
polígono40, g_6, q_7, j_6 = Polygon(Q_1, J_6, G_6)
polígono41, h_7, v_6, i_6 = Polygon(V_1, I_6, H_6)
polígono42, b_9, k_6, a_{10} = Polygon(K_6, A_2, B_2)
polígono43, f_8, e_8, e_9 = Polygon(E_2, E_6, F_2)
polígono44, m_8, l_6, n_7 = Polygon(L_6, N_6, M_6)
polígono45, n_8, o_6, o_2 = Polygon(O_6, O_2, N_2)
polígono46, r_7, p_7, q_8 = Polygon(P_6, Q_6, R_2)
polígono47, r_8, s_6, w_2 = Polygon(S_6, W_2, R_6)
polígono48, c_8, t_7, b_{10} = Polygon(T_6, B_3, C_3)
polígono49, f_9, g_7, u_7 = Polygon(G_3, U_6, F_3)
polígono50, z_6, v_7, w_6 = Polygon(V_6, W_6, Z_6)
polígono51, p_8, f_{10}, o_3 = Polygon(F_7, O_3, P_3)
polígono52, s_7, g_8, h_8 = Polygon(G_7, H_7, S_3)
polígono53, j_7, z_3, i_7 = Polygon(Z_3, I_7, J_7)
polígono54, c_9, d_8, k_7 = Polygon(D_4, K_7, C_4)
polígono55, g_9, h_9, l_7 = Polygon(H_4, L_7, G_4)
polígono56, d_9, c_{10}, e_{10} = Polygon(C_7, E_7, D_7)
polígono57, o_4, m_9, m_{10} = Polygon(M_4, M_7, O_4)
polígono58, t_8, n_9, r_9 = Polygon(N_7, R_4, T_4)
polígono59, z_4, v_8, o_7 = Polygon(V_4, O_7, Z_4)
polígono60, a_{11}, p_9, c_{11} = Polygon(P_7, C_5, A_5)
polígono61, e_{11}, q_9, g_{10} = Polygon(Q_7, G_5, E_5)
polígono62, r_{10}, l_8, j_8 = Polygon(L_5, J_5, R_7)
polígono63, n_{10}, p_{10}, s_8 = Polygon(P_5, S_7, N_5)
polígono64, s_9, t_9, q_{10} = Polygon(T_7, Q_5, S_5)
polígono65, l_9, k_8, i_8, i_9, U_7, V_7 = Polygon(L, K, 4.0)
j_9 = Segment(E, J)
k_9 = Segment(I, G)
ya = Sequence(Object["A" + (k)], k, 1.0, 32.0)
ya1 = KeepIf(x > 0.0, ya)
Z1 = Length(Union[{A1}, lista2])
Z2 = Length(Union[{A2}, lista2])
Z3 = Length(Union[{A3}, lista2])
Z4 = Length(Union[{A4}, lista2])
Z5 = Length(Union[{A5}, lista2])
Z6 = Length(Union[{A6}, lista2])
Z7 = Length(Union[{A7}, lista2])
Z8 = Length(Union[{A8}, lista2])
Z9 = Length(Union[{A9}, lista2])
Z10 = Length(Union[{A10}, lista2])
Z11 = Length(Union[{A11}, lista2])
Z12 = Length(Union[{A12}, lista2])
Z13 = Length(Union[{A13}, lista2])
Z14 = Length(Union[{A14}, lista2])
Z15 = Length(Union[{A15}, lista2])
Z16 = Length(Union[{A16}, lista2])
Z17 = Length(Union[{A17}, lista2])
Z18 = Length(Union[{A18}, lista2])
Z19 = Length(Union[{A19}, lista2])
Z20 = Length(Union[{A20}, lista2])
Z21 = Length(Union[{A21}, lista2])
Z22 = Length(Union[{A22}, lista2])
Z23 = Length(Union[{A23}, lista2])
Z24 = Length(Union[{A24}, lista2])
Z25 = Length(Union[{A25}, lista2])
Z26 = Length(Union[{A26}, lista2])
Z27 = Length(Union[{A27}, lista2])
Z28 = Length(Union[{A28}, lista2])
Z29 = Length(Union[{A29}, lista2])
Z30 = Length(Union[{A30}, lista2])
Z31 = Length(Union[{A31}, lista2])
Z32 = Length(Union[{A32}, lista2])
Y1 = KeepIf(x ≟ A1, ya1)
Y2 = KeepIf(x ≟ A2, ya1)
Y3 = KeepIf(x ≟ A3, ya1)
Y4 = KeepIf(x ≟ A4, ya1)
Y5 = KeepIf(x ≟ A5, ya1)
Y6 = KeepIf(x ≟ A6, ya1)
Y7 = KeepIf(x ≟ A7, ya1)
Y8 = KeepIf(x ≟ A8, ya1)
Y9 = KeepIf(x ≟ A9, ya1)
Y10 = KeepIf(x ≟ A10, ya1)
Y11 = KeepIf(x ≟ A11, ya1)
Y12 = KeepIf(x ≟ A12, ya1)
Y13 = KeepIf(x ≟ A13, ya1)
Y14 = KeepIf(x ≟ A14, ya1)
Y15 = KeepIf(x ≟ A15, ya1)
Y16 = KeepIf(x ≟ A16, ya1)
Y17 = KeepIf(x ≟ A17, ya1)
Y18 = KeepIf(x ≟ A18, ya1)
Y19 = KeepIf(x ≟ A19, ya1)
Y20 = KeepIf(x ≟ A20, ya1)
Y21 = KeepIf(x ≟ A21, ya1)
Y22 = KeepIf(x ≟ A22, ya1)
Y23 = KeepIf(x ≟ A23, ya1)
Y24 = KeepIf(x ≟ A24, ya1)
Y25 = KeepIf(x ≟ A25, ya1)
Y26 = KeepIf(x ≟ A26, ya1)
Y27 = KeepIf(x ≟ A27, ya1)
Y28 = KeepIf(x ≟ A28, ya1)
Y29 = KeepIf(x ≟ A29, ya1)
Y30 = KeepIf(x ≟ A30, ya1)
Y31 = KeepIf(x ≟ A31, ya1)
Y32 = KeepIf(x ≟ A32, ya1)
X1 = Length(Y1)
X2 = Length(Y2)
X3 = Length(Y3)
X4 = Length(Y4)
X5 = Length(Y5)
X6 = Length(Y6)
X7 = Length(Y7)
X8 = Length(Y8)
X9 = Length(Y9)
X10 = Length(Y10)
X11 = Length(Y11)
X12 = Length(Y12)
X13 = Length(Y13)
X14 = Length(Y14)
X15 = Length(Y15)
X16 = Length(Y16)
X17 = Length(Y17)
X18 = Length(Y18)
X19 = Length(Y19)
X20 = Length(Y20)
X21 = Length(Y21)
X22 = Length(Y22)
X23 = Length(Y23)
X24 = Length(Y24)
X25 = Length(Y25)
X26 = Length(Y26)
X27 = Length(Y27)
X28 = Length(Y28)
X29 = Length(Y29)
X30 = Length(Y30)
X31 = Length(Y31)
X32 = Length(Y32)
B1 = If(X1 > 1.0, "REPETIDO", If[Z1 ≟ 32.0, "BIEN", "?"])
B2 = If(X2 > 1.0, "REPETIDO", If[Z2 ≟ 32.0, "BIEN", "?"])
B3 = If(X3 > 1.0, "REPETIDO", If[Z3 ≟ 32.0, "BIEN", "?"])
B4 = If(X4 > 1.0, "REPETIDO", If[Z4 ≟ 32.0, "BIEN", "?"])
B5 = If(X5 > 1.0, "REPETIDO", If[Z5 ≟ 32.0, "BIEN", "?"])
B6 = If(X6 > 1.0, "REPETIDO", If[Z6 ≟ 32.0, "BIEN", "?"])
B7 = If(X7 > 1.0, "REPETIDO", If[Z7 ≟ 32.0, "BIEN", "?"])
B8 = If(X8 > 1.0, "REPETIDO", If[Z8 ≟ 32.0, "BIEN", "?"])
B9 = If(X9 > 1.0, "REPETIDO", If[Z9 ≟ 32.0, "BIEN", "?"])
B10 = If(X10 > 1.0, "REPETIDO", If[Z10 ≟ 32.0, "BIEN", "?"])
B11 = If(X11 > 1.0, "REPETIDO", If[Z11 ≟ 32.0, "BIEN", "?"])
B12 = If(X12 > 1.0, "REPETIDO", If[Z12 ≟ 32.0, "BIEN", "?"])
B13 = If(X13 > 1.0, "REPETIDO", If[Z13 ≟ 32.0, "BIEN", "?"])
B14 = If(X14 > 1.0, "REPETIDO", If[Z14 ≟ 32.0, "BIEN", "?"])
B15 = If(X15 > 1.0, "REPETIDO", If[Z15 ≟ 32.0, "BIEN", "?"])
B16 = If(X16 > 1.0, "REPETIDO", If[Z16 ≟ 32.0, "BIEN", "?"])
B17 = If(X17 > 1.0, "REPETIDO", If[Z17 ≟ 32.0, "BIEN", "?"])
B18 = If(X18 > 1.0, "REPETIDO", If[Z18 ≟ 32.0, "BIEN", "?"])
B19 = If(X19 > 1.0, "REPETIDO", If[Z19 ≟ 32.0, "BIEN", "?"])
B20 = If(X20 > 1.0, "REPETIDO", If[Z20 ≟ 32.0, "BIEN", "?"])
B21 = If(X21 > 1.0, "REPETIDO", If[Z21 ≟ 32.0, "BIEN", "?"])
B22 = If(X22 > 1.0, "REPETIDO", If[Z22 ≟ 32.0, "BIEN", "?"])
B23 = If(X23 > 1.0, "REPETIDO", If[Z23 ≟ 32.0, "BIEN", "?"])
B24 = If(X24 > 1.0, "REPETIDO", If[Z24 ≟ 32.0, "BIEN", "?"])
B25 = If(X25 > 1.0, "REPETIDO", If[Z25 ≟ 32.0, "BIEN", "?"])
B26 = If(X26 > 1.0, "REPETIDO", If[Z26 ≟ 32.0, "BIEN", "?"])
B27 = If(X27 > 1.0, "REPETIDO", If[Z27 ≟ 32.0, "BIEN", "?"])
B28 = If(X28 > 1.0, "REPETIDO", If[Z28 ≟ 32.0, "BIEN", "?"])
B29 = If(X29 > 1.0, "REPETIDO", If[Z29 ≟ 32.0, "BIEN", "?"])
B30 = If(X30 > 1.0, "REPETIDO", If[Z30 ≟ 32.0, "BIEN", "?"])
B31 = If(X31 > 1.0, "REPETIDO", If[Z31 ≟ 32.0, "BIEN", "?"])
B32 = If(X32 > 1.0, "REPETIDO", If[Z32 ≟ 32.0, "BIEN", "?"])
lista3 = Sequence(KeepIf[x ≟ Element[lista2, k], ya1], k, 1.0, 32.0)
lista4 = Sequence(Length[Element[lista3, k]], k, 1.0, 32.0)