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3.4.7 波浪博物馆：瓷砖7

3.4.7 波浪博物馆：瓷砖7
几何画板及绘图内容加载中，请稍等……
2023-03-22 22:32
圆向量解析几何变换几何作图
所属专题 geometriadinamica.es
①本范例演示了如何通过几何作图构建复杂的瓷砖图案，并展示其对称性；②涉及的核心数学概念包括微分方程、圆锥截面、代数、最大公约数与最小公倍数、单位圆；③作图要点——从下方『构造摘要』提炼用到了Line（线段）、Point（点）、OrthogonalLine（垂线）、Intersect（交点）、Midpoint（中点）、Mirror（镜像）、Min（最小值）、Rotate（旋转）、Vector（向量）、Translate（平移）等GeoGebra命令/对象；④适合高中数学教学，用于辅助学生理解几何变换与对称性在艺术设计中的应用。

GeoGebra 命令及参数

  1. Line(A, B) → b
  2. Line(G, b) → e
  3. Point(e) → J
  4. OrthogonalLine(J, e) → h
  5. OrthogonalLine(G, e) → f
  6. Point(f) → H
  7. OrthogonalLine(H, f) → g
  8. Intersect(g, h) → E
  9. Midpoint(E, H) → I
  10. Midpoint(I, E) → B_1
  11. Midpoint(G, J) → D
  12. Midpoint(J, E) → F
  13. Midpoint(H, G) → K
  14. Midpoint(D, I) → L
  15. Midpoint(K, L) → M
  16. Midpoint(L, F) → N
  17. Midpoint(F, J) → O
  18. Midpoint(J, D) → P
  19. Midpoint(G, D) → Q
  20. Midpoint(K, G) → R
  21. Midpoint(Q, M) → S
  22. Midpoint(L, D) → T
  23. Midpoint(P, N) → U
  24. Midpoint(F, E) → V
  25. Midpoint(K, H) → W
  26. Midpoint(W, V) → Z
  27. Midpoint(H, I) → A_1
  28. Midpoint(N, B_1) → C_1
  29. Midpoint(Z, W) → D_1
  30. Midpoint(D, U) → E_1
  31. Midpoint(U, J) → F_1
  32. Midpoint(T, Q) → G_1
  33. Midpoint(S, G) → H_1
  34. Midpoint(S, K) → I_1
  35. Midpoint(M, T) → J_1
  36. Midpoint(T, N) → K_1
  37. Midpoint(N, O) → L_1
  38. Midpoint(F, C_1) → M_1
  39. Midpoint(C_1, L) → N_1
  40. Midpoint(L, D_1) → O_1
  41. Midpoint(D_1, K) → P_1
  42. Midpoint(H, D_1) → Q_1
  43. Midpoint(D_1, I) → R_1
  44. Midpoint(I, C_1) → S_1
  45. Midpoint(C_1, E) → T_1
  46. Mirror(F_1, h) → U_1
  47. Mirror(L_1, h) → V_1
  48. Mirror(M_1, h) → W_1
  49. Mirror(T_1, h) → Z_1
  50. Mirror(B_1, h) → A_2
  51. Mirror(L_1, h) → C_2
  52. Line(Q, A_2) → d
  53. Line(F, d) → i
  54. Line(C_1, d) → k
  55. Line(S_1, k) → l
  56. Line(R_1, L_1) → j
  57. Line(D_1, j) → m
  58. Line(M, j) → n
  59. Line(I, j) → p
  60. Line(S, A_1) → t
  61. Line(E_1, N_1) → c_1
  62. Line(F_1, M_1) → d_1
  63. Line(G_1, R_1) → e_1
  64. Line(W_1, P_1) → g_1
  65. Line(Q_1, Z_1) → h_1
  66. Mirror(T, m) → T'
  67. Mirror(K_1, m) → I_2
  68. Mirror(T, m) → T'_1
  69. Mirror(L, m) → L'
  70. Mirror(T, m) → T'_2
  71. Mirror(U, m) → U'_1
  72. Mirror(T, m) → T'_3
  73. Point(b) → A1
  74. Min(90, ((a - 1) * 90)) → r1
  75. Rotate(T, ((-r1))°, T) → T'_7
  76. Rotate(U'_1, ((-r1))°, T) → D_{12}
  77. Rotate(T'_3, ((-r1))°, T) → E_{12}
  78. Rotate(U, ((-r1))°, T) → U'_3
  79. Rotate(T, ((-r1))°, T) → T'_8
  80. Rotate(T, ((-r1))°, T'_8) → T'_9
  81. Rotate(T'_2, ((-r1))°, T) → I_{12}
  82. Rotate(T'_1, ((-r1))°, T) → T_{12}
  83. Rotate(L', ((-r1))°, T) → L''_2
  84. Rotate(L, ((-r1))°, T) → L'_2
  85. Midpoint(C_1, E) → K_{20}
  86. Rotate(U'_1, 270°, L') → D_{21}
  87. Rotate(D_{21}, 270°, L') → G_{21}
  88. Rotate(G_{21}, 270°, L') → M_{21}
  89. Line(U'_1, D_{21}) → n_1
  90. Mirror(U'_1, n_1) → V_{21}
  91. Mirror(M_{21}, n_1) → D_{22}
  92. Mirror(D_{21}, n_1) → M_{24}
  93. Mirror(G_{21}, n_1) → P_{24}
  94. Min(180, ((a - 1) * 180)) → r2
  95. Min(270, ((a - 1) * 270)) → r3
  96. Rotate(T, r1°, T) → T'_4
  97. Rotate(T, r2°, T) → T'_5
  98. Rotate(T, r3°, T) → T'_6
  99. Rotate(L, r1°, T) → L'_1
  100. Rotate(K_1, r1°, T) → Q_3
  101. Rotate(L, r2°, T) → L'_3
  102. Rotate(K_1, r2°, T) → Z_3
  103. Rotate(L, r3°, T) → L'_4
  104. Rotate(K_1, r3°, T) → H_4
  105. Min(180, ((a - 5.5) * 180)) → r4
  106. Intersect(t, i) → H_{15}
  107. Midpoint(H_{15}, D) → J_{15}
  108. Vector(S, D) → u
  109. Vector(S, L) → w
  110. Vector(U, P) → z
  111. Vector(U, O) → u_1
  112. Translate(pic1, u_1) → pic1'
  113. Translate(pic1', z) → pic1''
  114. Translate(pic1, z) → pic1'_1
  115. Translate(pic1'_1, z) → pic2
  116. Translate(pic2, z) → pic2'
  117. Translate(pic2', z) → pic2''
  118. Translate(pic2'', u_1) → pic2'''
  119. Translate(pic2''', u_1) → pic3
  120. Translate(pic2', u_1) → pic2''_1
  121. Translate(pic2''_1, u_1) → pic4
  122. Translate(pic2, u_1) → pic2'_1
  123. Translate(pic3, u_1) → pic3'
  124. Translate(pic3', u_1) → pic3''
  125. Translate(pic4, u_1) → pic4'
  126. Translate(pic4', u_1) → pic4''
  127. Translate(pic2'_1, u_1) → pic5
  128. Translate(pic5, u_1) → pic5'
  129. Translate(pic5', u_1) → pic5''
  130. Translate(pic1'', u_1) → pic1'''
  131. Translate(pic1''', u_1) → pic6
  132. Translate(pic6, u_1) → pic6'
  133. Translate(pic1', u_1) → pic1''_1
  134. Translate(pic1''_1, u_1) → pic7
  135. Translate(pic7, u_1) → pic7'
  136. Midpoint(Q, S) → C
  137. Midpoint(S, M) → B_2
  138. Midpoint(M, D_1) → D_2
  139. Midpoint(D, T) → E_2
  140. Midpoint(T, L) → F_2
  141. Midpoint(L, Z) → G_2
  142. Midpoint(G_1, J_1) → H_2
  143. Midpoint(J_1, O_1) → J_2
  144. Midpoint(O_1, R_1) → K_2
  145. Midpoint(E_1, F_1) → L_2
  146. Midpoint(U, N) → M_2
  147. Midpoint(N, C_1) → N_2
  148. Midpoint(T_1, M_1) → O_2
  149. Midpoint(M_1, L_1) → P_2
  150. Midpoint(L_1, F_1) → Q_2
  151. Midpoint(J, O) → R_2
  152. Midpoint(O, F) → S_2
  153. Midpoint(F, V) → T_2
  154. Line(E_2, i) → q
  155. Line(C, d) → r
  156. Line(B_2, k) → s
  157. Line(S_2, p) → a_1
  158. Line(Q_2, j) → b_1
  159. Line(L_2, m) → f_1
  160. Line(E_2, n) → i_1
  161. Line(T_2, p) → j_1
  162. Line(L_2, i) → k_1
  163. Line(D_2, l) → l_1
  164. Intersect(r, b_1) → U_2
  165. Intersect(q, f_1) → V_2
  166. Intersect(s, a_1) → W_2

AI 绘图提示语参考

绘制一个复杂的瓷砖图案，包含多个对称点和线。首先画两条线b和e，然后在e上取点J，通过J画两条垂直线h和f，分别在f和h上取点H和E。接着找到E和H的中点I，以此类推，通过一系列中点构造多个点，最终通过镜像操作生成对称点，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。