Amazing Patterns

Amazing Patterns
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2020-02-06 16:41
This example demonstrates geometric patterns constructed through polygons and prisms. It involves core mathematical concepts such as logarithms, combinatorics, translation, histograms, and the Pythagorean theorem. The construction utilizes GeoGebra commands like Polygon and Prism, along with objects like I_3, H_3, U_2, T_2, S_2, R_2, Q_2, G_2, P_2, O_2, N_2, M_2, L_2, J_2, I_2, H_2, S_1, R_1, D_1, C_1, B_1, A_1, Z, W, V, U, T, L, K, J, H, G, F, E, E_1, F_1, G_1, H_1, I_1, N_1. It is suitable for high school and above, focusing on geometric transformations and solid geometry.

GeoGebra Commands & Parameters

  1. Polygon(E_2, F_2, O_1, I_1, H_1, G_1, F_1, E_1, D_1, I_3, K, J, O_2, H, G, F, E, C_1, B_1, A_1, Z, W, V, P_2, U, T, S_1, R_1, Q_1, H_3, A_3, B_3, C_3, D_3, W_1, E_3, F_3, G_3, N_1, L, G_2, Q_2, R_2, S_2, T_2, V_1, U_2, H_2, I_2, J_2, K_2, L_2, M_2, N_2, D_2, Z_1, B_2, A_2, C_2) → poly3, j, t, a, b, c, d, e, f_1, g_1, h_1, i_1, k, j_1, k_1, l_1, m_1, n_1, p_1, q_1, r_1, s_1, t_1, l, a_1, b_1, c_1, d_1, e_1, f_2, g_2, h_2, i_2, j_2, m, k_2, l_2, m_2, n_2, p_2, q_2, r_2, s_2, t_2, a_2, n, b_2, c_2, d_2, e_2, f_3, g_3, h_3, i_3, j_3, k_3, p, q, r, s
  2. Prism(poly3, g) → h, W_4, H_5, face118, face119, face105, face94, face71, face70, face69, face68, face67, face65, I_5, face66, face81, face79, face80, face78, face77, face75, face76, face112, face120, J_5, edge157, edge158, edge117, edge116, edge151, edge150, edge152, edge154, edge153, edge155, K_5, edge148, edge146, edge145, edge144, edge143, edge142, edge126, edge108, edge136, edge137, L_5, edge138, edge139, edge140, edge141, edge127, edge128, edge129, edge130, edge131, edge132, M_5, edge133, edge134, edge124, edge125, edge149, edge109, edge159, edge160, edge161, edge162, N_5, edge163, edge164, edge165, edge147, edge135, edge115, edge114, edge113, edge112, edge111, O_5, edge110, edge123, edge122, edge121, edge166, edge120, edge119, edge118, edge156, edge167, P_5, edge169, edge170, edge171, edge172, edge173, edge174, edge175, edge176, edge177, edge178, Q_5, edge179, edge180, edge181, edge182, edge183, edge184, edge185, edge186, edge187, edge188, Z_4, R_5, edge189, edge190, edge191, edge192, edge193, edge194, edge195, edge196, edge197, edge198, S_5, edge199, edge200, edge201, edge202, edge203, edge204, edge205, edge206, edge207, edge208, T_5, edge209, edge210, edge211, edge212, edge213, edge214, edge215, edge216, edge217, edge218, U_5, edge219, edge220, edge221, edge222, edge223, edge224, edge225, edge168, V_5, W_5, Z_5, A_6, B_6, C_6, A_5, D_6, E_6, F_6, G_6, H_6, I_6, J_6, K_6, L_6, M_6, B_5, N_6, O_6, P_6, Q_6, R_6, S_6, T_6, U_6, V_6, W_6, C_5, Z_6, A_7, B_7, C_7, D_7, E_7, F_7, G_7, H_7, I_7, D_5, face113, face74, face72, face73, face107, face108, face109, face110, face111, face106, E_5, face104, face103, face102, face101, face100, face85, face61, face62, face95, face96, F_5, face97, face98, face99, face87, face86, face88, face89, face90, face91, face92, G_5, face93, face83, face82, face84, face63, face64, face114, face115, face116, face117
  3. Polygon(A, B, C, D, I, M, N, O, P, Q) → poly1, a_3, q_3, b_3, c_3, d_3, i, m_3, n_3, o, p_3
  4. Prism(poly1, u) → v, W_2, Q_3, face11, face13, face14, face15, face16, face17, face18, face19, face20, Z_2, face12, face21, edge18, edge19, edge20, edge21, edge22, edge23, edge24, edge25, J_3, edge26, edge27, edge28, edge30, edge31, edge32, edge33, edge34, edge35, edge36, K_3, edge37, edge29, L_3, M_3, N_3, O_3, P_3

AI Drawing Prompt Reference

Create a complex geometric pattern using polygons and prisms to demonstrate geometric transformations and solid geometry concepts. Start by drawing multiple polygons connected by points, then use the prism command to generate three-dimensional structures based on these polygons, showcasing geometric transformations and spatial relationships, resulting in a立体 and symmetrical artistic piece.
The prompt above was compiled from the original drawing commands and is for reference only.