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21. Mosaico. La Alhambra

21. Mosaico. La Alhambra
几何画板及绘图内容加载中，请稍等……
2023-03-20 19:58
多边形解析几何几何作图
所属专题 geometriadinamica.es
这个范例展示了马约拉拉布的几何图案构造，涉及三角形、圆和多边形的组合。核心数学概念包括几何作图、变换和坐标几何。作图要点包括使用GeoGebra命令如If、Line、OrthogonalLine等来构造图形。适合初中或高中数学课程，用于学习几何变换和图形分析。

GeoGebra 命令及参数

  1. If(paso > 0 ∧ paso < 7, 1, 0) → t_1
  2. If(paso > 1 ∧ paso < 7, 1, 0) → t_2
  3. If(paso > 2 ∧ paso < 7, 1, 0) → t_3
  4. If(paso > 3 ∧ paso < 7, 1, 0) → t_4
  5. If(paso > 4 ∧ paso < 7, 1, 0) → t_5
  6. If(paso > 5 ∧ paso < 7, 1, 0) → t_6
  7. Line(H1, H2) → a
  8. Line(A, a) → b
  9. OrthogonalLine(A, a) → c
  10. Point(b) → B
  11. Dilate(B, pr, A) → Dil
  12. Circle(A, Dil) → d
  13. Intersect(d, c) → D5, C
  14. OrthogonalLine(C, c) → e
  15. OrthogonalLine(B, b) → f
  16. Intersect(f, e) → D
  17. Polygon(A, B, D, C) → P, a_1, b_1, d_1, c_1
  18. OrthogonalLine(B_1, a_1) → g
  19. Line(E, g) → h
  20. Point(h) → F
  21. Point(g) → H
  22. Point(g) → I
  23. Vector(F, H) → u
  24. Vector(F, I) → v
  25. Line(B_2, a_1) → i
  26. Line(M, i) → j
  27. Line(J, i) → k
  28. OrthogonalLine(K, i) → l
  29. OrthogonalLine(L, i) → m
  30. Intersect(l, k) → R1
  31. Intersect(m, k) → R2
  32. Intersect(m, j) → R4
  33. Intersect(l, j) → R3
  34. Intersect(l, i) → R5
  35. Intersect(m, i) → R6
  36. Line(G, i) → n
  37. Line(N, i) → p
  38. Line(O, i) → q
  39. Point(q) → S3
  40. Point(q) → S2
  41. Point(q) → S1
  42. Point(p) → S6
  43. Point(p) → S5
  44. Point(p) → S4
  45. Point(n) → S9
  46. Point(n) → S8
  47. Point(n) → S7
  48. Point(i) → Q
  49. Point(j) → R
  50. Point(k) → S
  51. Point(m) → T
  52. Line(B_3, c_1) → r
  53. Line(T, r) → s
  54. OrthogonalLine(Q, r) → t
  55. OrthogonalLine(R, r) → e_1
  56. OrthogonalLine(S, r) → f_1
  57. OrthogonalLine(B_4, a_1) → g_1
  58. OrthogonalLine(S7, g_1) → h_1
  59. OrthogonalLine(S4, g_1) → i_1
  60. OrthogonalLine(S1, g_1) → j_1
  61. Line(S8, g_1) → k_1
  62. Line(S9, g_1) → l_1
  63. Rotate(g_1, 45°, B_4) → m_1
  64. Intersect(k_1, e_1) → U
  65. Intersect(k_1, f_1) → V
  66. Line(U, m_1) → n_1
  67. Line(V, m_1) → p_1
  68. Intersect(k_1, t) → W
  69. Line(W, m_1) → q_1
  70. OrthogonalLine(W, m_1) → r_1
  71. OrthogonalLine(U, m_1) → s_1
  72. OrthogonalLine(V, m_1) → a_2
  73. Intersect(r, j_1) → Y
  74. OrthogonalLine(Y, m_1) → b_2
  75. OrthogonalLine(B_5, b_1) → c_2
  76. Point(c_2) → Z
  77. Intersect(c_2, s) → C_1
  78. Point(k_1) → D_1
  79. Point(j_1) → E_1
  80. Point(j_1) → F_1
  81. Point(l_1) → G_1
  82. Polygon(C_1, D_1, S2, E_1, R2, F_1, S3, G_1) → P_1, c_3, d_2, s2, e_2, r2, f_2, s3, g_2
  83. Point(c_2) → K_1
  84. OrthogonalLine(B_6, c_1) → h_2
  85. Point(h_2) → M_1
  86. Point(g_1) → H_1
  87. Point(j_1) → J_1
  88. Point(j_1) → L_1
  89. Point(d_2) → N_1
  90. Point(k_1) → O_1
  91. Intersect(h_2, s) → R_1
  92. Point(i_1) → S_1
  93. Point(k_1) → T_1
  94. Point(l_1) → U_1
  95. Point(i_1) → V_1
  96. Polygon(R_1, S_1, S5, T_1, R4, U_1, S6, V_1) → W_1, r_2, s_2, s5, t_7, r4, u_1, s6, v_1
  97. Point(h_2) → Y_1
  98. Point(r) → Z_1
  99. Polygon(Y_1, H_1, S1, J_1, Z_1, L_1, N_1, O_1) → P_2, y_1, h_4, s1_1, j_3, z_1, l_3, n_3, o_2
  100. Point(g_1) → I_1
  101. Point(i_1) → Q_1
  102. Point(i_1) → C_2
  103. Point(s5) → D_2
  104. Point(k_1) → E_2
  105. Polygon(Y_1, I_1, S4, Q_1, R3, C_2, D_2, E_2) → Q_2, y_2, i_2, s4, q_2, r3, c_4, d_3, e_3
  106. Point(h_2) → F_2
  107. Polygon(F_2, I_1, S4, Q_1, R3, C_2, D_2, E_2) → R_2, f_3, i_3, s4_1, q_3, r3_1, c_5, d_4, e_4
  108. Polygon(F_2, H_1, S1, J_1, Z_1, L_1, N_1, O_1) → S_2, f_4, h_3, s1, j_2, z_2, l_2, n_2, o_1

AI 绘图提示语参考

绘制一个由三角形、圆和多边形组成的几何图案，首先通过点A和点H2之间的线段构造直线a，然后利用点A和直线a构造直线b，接着构造直线b的垂线c，并在直线c上找到点B。通过点B和点A进行相似变换得到点Dil，再以点A和点Dil为半径构造圆d，找到圆d和直线c的交点D5和C。接着构造C的垂线e和B的垂线f，找到它们的交点D，然后用点A、B、D、C构造多边形P。继续构造多边形P的边的垂线，找到新的点F、H、I，通过这些点构造新的线段和多边形，最终形成复杂的几何图案。
以上提示语为根据原始绘图命令整理而来，仅供参考。