Pythagoras' Tree Demonstration

GeoGebra Commands & Parameters

1. Midpoint(A, B) → C
2. Rotate(B, α, C) → B'
3. Polygon(B', B, 4) → poly1, b', b, a, c, D, E
4. Polygon(A, B', 4) → poly2, a_1, b'_1, d, e, F, G
5. Midpoint(E, D) → H
6. Midpoint(G, F) → I
7. Rotate(D, α, H) → D'
8. Rotate(F, α, I) → F'
9. Polygon(D', D, 4) → poly3, d', d_1, f, g, J, K
10. Polygon(E, D', 4) → poly4, e_1, d'_1, h, i, L, M
11. Polygon(F', F, 4) → poly5, f', f_1, j, k, N, O
12. Polygon(G, F', 4) → poly6, g_1, f'_1, l, m, P, Q
13. Tool1(K, J, α) → R, S, D_1, E_1, F_1, G_1, H_1, I_1, J_1, K_1, poly7, poly8, T, poly9, poly10, poly11, poly12, U, V, W, Z, A_1, B_1, C_1
14. Tool1(M, L, α) → L_1, M_1, V_1, W_1, Z_1, A_2, B_2, C_2, D_2, E_2, poly13, poly14, N_1, poly15, poly16, poly17, poly18, O_1, P_1, Q_1, R_1, S_1, T_1, U_1
15. Tool1(O, N, α) → F_2, G_2, P_2, Q_2, R_2, S_2, T_2, U_2, V_2, W_2, poly19, poly20, H_2, poly21, poly22, poly23, poly24, I_2, J_2, K_2, L_2, M_2, N_2, O_2
16. Tool1(Q, P, α) → Z_2, A_3, J_3, K_3, L_3, M_3, N_3, O_3, P_3, Q_3, poly25, poly26, B_3, poly27, poly28, poly29, poly30, C_3, D_3, E_3, F_3, G_3, H_3, I_3
17. Tool1(E_1, D_1, α) → R_3, S_3, D_4, E_4, F_4, G_4, H_4, I_4, J_4, K_4, poly31, poly32, T_3, poly33, poly34, poly35, poly36, U_3, V_3, W_3, Z_3, A_4, B_4, C_4
18. Tool1(G_1, F_1, α) → L_4, M_4, V_4, W_4, Z_4, A_5, B_5, C_5, D_5, E_5, poly37, poly38, N_4, poly39, poly40, poly41, poly42, O_4, P_4, Q_4, R_4, S_4, T_4, U_4
19. Tool1(I_1, H_1, α) → F_5, G_5, P_5, Q_5, R_5, S_5, T_5, U_5, V_5, W_5, poly43, poly44, H_5, poly45, poly46, poly47, poly48, I_5, J_5, K_5, L_5, M_5, N_5, O_5
20. Tool1(K_1, J_1, α) → Z_5, A_6, J_6, K_6, L_6, M_6, N_6, O_6, P_6, Q_6, poly49, poly50, B_6, poly51, poly52, poly53, poly54, C_6, D_6, E_6, F_6, G_6, H_6, I_6
21. Tool1(W_1, V_1, α) → R_6, S_6, D_7, E_7, F_7, G_7, H_7, I_7, J_7, K_7, poly55, poly56, T_6, poly57, poly58, poly59, poly60, U_6, V_6, W_6, Z_6, A_7, B_7, C_7
22. Tool1(A_2, Z_1, α) → L_7, M_7, V_7, W_7, Z_7, A_8, B_8, C_8, D_8, E_8, poly61, poly62, N_7, poly63, poly64, poly65, poly66, O_7, P_7, Q_7, R_7, S_7, T_7, U_7
23. Tool1(C_2, B_2, α) → F_8, G_8, P_8, Q_8, R_8, S_8, T_8, U_8, V_8, W_8, poly67, poly68, H_8, poly69, poly70, poly71, poly72, I_8, J_8, K_8, L_8, M_8, N_8, O_8
24. Tool1(E_2, D_2, α) → Z_8, A_9, J_9, K_9, L_9, M_9, N_9, O_9, P_9, Q_9, poly73, poly74, B_9, poly75, poly76, poly77, poly78, C_9, D_9, E_9, F_9, G_9, H_9, I_9
25. Tool1(Q_2, P_2, α) → R_9, S_9, D_{10}, E_{10}, F_{10}, G_{10}, H_{10}, I_{10}, J_{10}, K_{10}, poly79, poly80, T_9, poly81, poly82, poly83, poly84, U_9, V_9, W_9, Z_9, A_{10}, B_{10}, C_{10}
26. Tool1(S_2, R_2, α) → L_{10}, M_{10}, V_{10}, W_{10}, Z_{10}, A_{11}, B_{11}, C_{11}, D_{11}, E_{11}, poly85, poly86, N_{10}, poly87, poly88, poly89, poly90, O_{10}, P_{10}, Q_{10}, R_{10}, S_{10}, T_{10}, U_{10}
27. Tool1(U_2, T_2, α) → F_{11}, G_{11}, P_{11}, Q_{11}, R_{11}, S_{11}, T_{11}, U_{11}, V_{11}, W_{11}, poly91, poly92, H_{11}, poly93, poly94, poly95, poly96, I_{11}, J_{11}, K_{11}, L_{11}, M_{11}, N_{11}, O_{11}
28. Tool1(W_2, V_2, α) → Z_{11}, A_{12}, J_{12}, K_{12}, L_{12}, M_{12}, N_{12}, O_{12}, P_{12}, Q_{12}, poly97, poly98, B_{12}, poly99, poly100, poly101, poly102, C_{12}, D_{12}, E_{12}, F_{12}, G_{12}, H_{12}, I_{12}
29. Tool1(K_3, J_3, α) → R_{12}, S_{12}, D_{13}, E_{13}, F_{13}, G_{13}, H_{13}, I_{13}, J_{13}, K_{13}, poly103, poly104, T_{12}, poly105, poly106, poly107, poly108, U_{12}, V_{12}, W_{12}, Z_{12}, A_{13}, B_{13}, C_{13}
30. Tool1(M_3, L_3, α) → L_{13}, M_{13}, V_{13}, W_{13}, Z_{13}, A_{14}, B_{14}, C_{14}, D_{14}, E_{14}, poly109, poly110, N_{13}, poly111, poly112, poly113, poly114, O_{13}, P_{13}, Q_{13}, R_{13}, S_{13}, T_{13}, U_{13}
31. Tool1(O_3, N_3, α) → F_{14}, G_{14}, P_{14}, Q_{14}, R_{14}, S_{14}, T_{14}, U_{14}, V_{14}, W_{14}, poly115, poly116, H_{14}, poly117, poly118, poly119, poly120, I_{14}, J_{14}, K_{14}, L_{14}, M_{14}, N_{14}, O_{14}
32. Tool1(Q_3, P_3, α) → Z_{14}, A_{15}, J_{15}, K_{15}, L_{15}, M_{15}, N_{15}, O_{15}, P_{15}, Q_{15}, poly121, poly122, B_{15}, poly123, poly124, poly125, poly126, C_{15}, D_{15}, E_{15}, F_{15}, G_{15}, H_{15}, I_{15}