三角形铺砖模式探究

三角形铺砖模式探究
几何画板及绘图内容加载中,请稍等……
2014-07-14 22:05
①本范例演示通过旋转等边三角形进行铺砖,观察图形模式;②涉及核心数学概念包括多边形、等边三角形、几何变换、三角函数等;③作图要点使用 GeoGebra 命令 Point, Polygon, Segment, Intersect, Rotate 构造三角形及旋转变换;④适合初中及以上学生用于几何变换和图案探索的数学活动。

GeoGebra 命令及参数

  1. Point(Circle[D_1, 3.9400507610943287]) → E_1
  2. Polygon(D_1, E_1, F_1) → poly2_1, f_1, d_1, e_1
  3. Segment(D_1, E_1) → a_1
  4. Intersect(d_1, e_1) → C_1
  5. Point(Circle[A, f_1]) → B
  6. Rotate(B + (d_1, 0), Angle[F_1 - E_1] + Angle[B - A] - Angle[E_1 - D_1], B) → C
  7. Polygon(A, B, C) → poly1, c, a, b
  8. Point(Circle[D, f_1]) → E
  9. Rotate(E + (d_1, 0), Angle[F_1 - E_1] + Angle[E - D] - Angle[E_1 - D_1], E) → F
  10. Polygon(D, E, F) → poly2, f, d, e
  11. Point(Circle[G, f_1]) → H
  12. Rotate(H + (d_1, 0), Angle[F_1 - E_1] + Angle[H - G] - Angle[E_1 - D_1], H) → I
  13. Polygon(G, H, I) → poly3, i, g, h
  14. Point(Circle[J, f_1]) → K
  15. Rotate(K + (d_1, 0), Angle[F_1 - E_1] + Angle[K - J] - Angle[E_1 - D_1], K) → L
  16. Polygon(J, K, L) → poly4, l, j, k
  17. Point(Circle[M, f_1]) → N
  18. Rotate(N + (d_1, 0), Angle[F_1 - E_1] + Angle[N - M] - Angle[E_1 - D_1], N) → O
  19. Polygon(M, N, O) → poly5, o, m, n
  20. Point(Circle[P, f_1]) → Q
  21. Rotate(Q + (d_1, 0), Angle[F_1 - E_1] + Angle[Q - P] - Angle[E_1 - D_1], Q) → R
  22. Polygon(P, Q, R) → poly6, r, p, q
  23. Point(Circle[S, f_1]) → T
  24. Rotate(T + (d_1, 0), Angle[F_1 - E_1] + Angle[T - S] - Angle[E_1 - D_1], T) → U
  25. Polygon(S, T, U) → poly7, u, s, t
  26. Point(Circle[V, f_1]) → W
  27. Rotate(W + (d_1, 0), Angle[F_1 - E_1] + Angle[W - V] - Angle[E_1 - D_1], W) → Z
  28. Polygon(V, W, Z) → poly8, z, v, w
  29. Point(Circle[A_1, f_1]) → B_1
  30. Rotate(B_1 + (d_1, 0), Angle[F_1 - E_1] + Angle[B_1 - A_1] - Angle[E_1 - D_1], B_1) → G_1
  31. Polygon(A_1, B_1, G_1) → poly9, g_1, a_2, b_1
  32. Point(Circle[H_1, f_1]) → I_1
  33. Rotate(I_1 + (d_1, 0), Angle[F_1 - E_1] + Angle[I_1 - H_1] - Angle[E_1 - D_1], I_1) → J_1
  34. Polygon(H_1, I_1, J_1) → poly10, j_1, h_1, i_1
  35. Point(Circle[K_1, f_1]) → L_1
  36. Rotate(L_1 + (d_1, 0), Angle[F_1 - E_1] + Angle[L_1 - K_1] - Angle[E_1 - D_1], L_1) → M_1
  37. Polygon(K_1, L_1, M_1) → poly11, m_1, k_1, l_1
  38. Point(Circle[N_1, f_1]) → O_1
  39. Rotate(O_1 + (d_1, 0), Angle[F_1 - E_1] + Angle[O_1 - N_1] - Angle[E_1 - D_1], O_1) → P_1
  40. Polygon(N_1, O_1, P_1) → poly12, p_1, n_1, o_1
  41. Point(Circle[Q_1, f_1]) → R_1
  42. Rotate(R_1 + (d_1, 0), Angle[F_1 - E_1] + Angle[R_1 - Q_1] - Angle[E_1 - D_1], R_1) → S_1
  43. Polygon(Q_1, R_1, S_1) → poly13, s_1, q_1, r_1
  44. Point(Circle[T_1, f_1]) → U_1
  45. Rotate(U_1 + (d_1, 0), Angle[F_1 - E_1] + Angle[U_1 - T_1] - Angle[E_1 - D_1], U_1) → V_1
  46. Polygon(T_1, U_1, V_1) → poly14, v_1, t_1, u_1
  47. Point(Circle[W_1, f_1]) → Z_1
  48. Rotate(Z_1 + (d_1, 0), Angle[F_1 - E_1] + Angle[Z_1 - W_1] - Angle[E_1 - D_1], Z_1) → A_2
  49. Polygon(W_1, Z_1, A_2) → poly15, a_3, w_1, z_1
  50. Point(Circle[B_2, f_1]) → C_2
  51. Rotate(C_2 + (d_1, 0), Angle[F_1 - E_1] + Angle[C_2 - B_2] - Angle[E_1 - D_1], C_2) → E_2
  52. Polygon(B_2, C_2, E_2) → poly16, e_2, b_2, c_2

AI 绘图提示语参考

绘制一个由旋转的等边三角形组成的几何图案。首先创建一个等边三角形,然后围绕其顶点依次旋转并绘制多个相同的三角形,形成一种规律的镶嵌效果。每个新三角形都是基于前一个三角形旋转一定角度得到的,展示出旋转对称和几何变换的美感。
以上提示语为根据原始绘图命令整理而来,仅供参考。