Azra三角形

Azra三角形
几何画板及绘图内容加载中,请稍等……
2019-11-20 01:26
所属专题 Pyramid Puzzles
该范例演示了Azra三角形的构造。涉及的核心数学概念包括三角形的性质和几何作图。通过使用GeoGebra命令如Polygon、Midpoint等,可以动态地展示三角形的构造过程。适合初中及以上学生学习三角形的相关知识。

GeoGebra 命令及参数

  1. Polygon(A, B, 4) → poly1, f_5, g, h, i, C, D
  2. Polygon(D, C, 4) → poly3, n, p, q, r, G, H
  3. Polygon(H, G, 4) → poly4, s, t, a_4, b_4, I, J
  4. Polygon(J, I, 4) → poly5, c_4, d_4, e_4, f_1, K, L
  5. Polygon(L, K, 4) → poly6, g_1, h_1, i_1, j_1, M, N
  6. Polygon(N, M, 4) → poly2, j, k, l, m, E, F
  7. Midpoint(i) → O
  8. Midpoint(r) → P
  9. Midpoint(b_4) → Q
  10. Midpoint(f_1) → R
  11. Midpoint(j_1) → S
  12. Midpoint(m) → T
  13. Midpoint(m) → U
  14. Polygon(O, P, 4) → poly7, k_1, l_1, m_1, n_1, V, W
  15. Polygon(P, Q, 4) → poly8, p_1, q_1, r_1, s_1, Z, A_1
  16. Polygon(Q, R, 4) → poly9, t_1, a_1, b_1, c_1, B_1, C_1
  17. Polygon(R, S, 4) → poly10, d_1, e_1, f_2, g_2, D_1, E_1
  18. Polygon(S, T, 4) → poly11, h_2, i_2, j_2, k_2, F_1, G_1
  19. Midpoint(m_1) → H_1
  20. Midpoint(r_1) → I_1
  21. Midpoint(b_1) → J_1
  22. Polygon(H_1, I_1, 4) → poly12, l_2, m_2, n_2, p_2, K_1, L_1
  23. Polygon(I_1, J_1, 4) → poly13, q_2, r_2, s_2, t_2, M_1, N_1
  24. Midpoint(f_2) → P_1
  25. Midpoint(j_2) → Q_1
  26. Midpoint(j_2) → R_1
  27. Polygon(J_1, P_1, 4) → poly14, a_2, b_2, c_2, d_2, O_1, S_1
  28. Polygon(P_1, Q_1, 4) → poly15, e_2, f_3, g_3, h_3, T_1, U_1
  29. Midpoint(n_2) → V_1
  30. Midpoint(s_2) → W_1
  31. Midpoint(c_2) → Z_1
  32. Polygon(V_1, W_1, 4) → poly16, i_3, j_3, k_3, l_3, A_2, B_2
  33. Polygon(W_1, Z_1, 4) → poly17, m_3, n_3, p_3, q_3, C_2, D_2
  34. Midpoint(g_3) → E_2
  35. Polygon(Z_1, E_2, 4) → poly18, r_3, s_3, t_3, a_3, F_2, G_2
  36. Midpoint(k_3) → H_2
  37. Midpoint(p_3) → I_2
  38. Midpoint(t_3) → J_2
  39. Polygon(H_2, I_2, 4) → poly19, b_3, c_3, d_3, e_3, K_2, L_2
  40. Polygon(I_2, J_2, 4) → poly20, f_4, g_4, h_4, i_4, M_2, N_2
  41. Midpoint(d_3) → O_2
  42. Midpoint(h_4) → P_2
  43. Polygon(O_2, P_2, 4) → poly21, j_4, k_4, l_4, m_4, Q_2, R_2

AI 绘图提示语参考

绘制一个由四个小三角形组成的Azra三角形。首先,使用点A、B、C、D、E、F、G、H、I、J、K、L、M、N、O、P、Q、R、S、T、U、V、W、X、Y、Z作为顶点,依次构造五个大三角形,每个大三角形由四个小三角形组成。接着,找到每个大三角形的中点,构造新的小三角形,重复此过程,直到所有小三角形都构造完毕。
以上提示语为根据原始绘图命令整理而来,仅供参考。