Zoom in Golden Rectangle (infinite loop)

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2017-06-21 05:52

This example demonstrates the infinite loop of continuously zooming into a golden rectangle, illustrating the concept of golden ratio, continuity, logarithmic functions, and similarity transformations. It uses GeoGebra commands like Polygon, Segment, and Intersect to construct nested golden rectangles, providing an intuitive understanding of continuity and geometric transformations for high school and above learners.

GeoGebra Commands & Parameters

Polygon(C, O, 4) → poly1, f, g, h, i, D, E
Segment(C, A) → j
Segment(B, D) → k
Polygon(B, E, 4) → poly2, l, m, n, q, F, G
Intersect(k, n) → H
Polygon(G, H, 4) → poly3, r, s, t, a, I, J
Intersect(j, s) → K
Polygon(I, K, 4) → poly4, b, c, d, e, L, M
Polygon(F, L, 4) → poly5, f_1, g_1, h_1, i_1, N, P
Polygon(H, P, 4) → poly6, j_1, k_1, l_1, m_1, Q, R
Polygon(K, R, 4) → poly7, n_1, p_1, q_1, r_1, S, T
Polygon(N, T, 4) → poly8, s_1, t_1, a_1, b_1, U, V
Polygon(Q, V, 4) → poly9, c_1, d_1, e_1, f_2, W, Z
Polygon(S, Z, 4) → poly10, g_2, h_2, i_2, j_2, A_1, B_1
Polygon(U, B_1, 4) → poly11, k_2, l_2, m_2, n_2, C_1, D_1
Polygon(W, D_1, 4) → poly12, p_2, q_2, r_2, s_2, E_1, F_1
Polygon(A_1, F_1, 4) → poly13, t_2, a_2, b_2, c_2, G_1, H_1
Polygon(C_1, H_1, 4) → poly14, d_2, e_2, f_3, g_3, I_1, J_1
Polygon(E_1, J_1, 4) → poly15, h_3, i_3, j_3, k_3, K_1, L_1
Polygon(G_1, L_1, 4) → poly16, l_3, m_3, n_3, p_3, M_1, N_1
Polygon(I_1, N_1, 4) → poly17, q_3, r_3, s_3, t_3, O_1, P_1
Polygon(K_1, P_1, 4) → poly18, a_3, b_3, c_3, d_3, Q_1, R_1
Polygon(M_1, R_1, 4) → poly19, e_3, f_4, g_4, h_4, S_1, T_1
Polygon(O_1, T_1, 4) → poly20, i_4, j_4, k_4, l_4, U_1, V_1
Polygon(Q_1, V_1, 4) → poly21, m_4, n_4, p_4, q_4, W_1, Z_1
Intersect(j, k) → Z0