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3.4.1(b) 欧纳博物馆：瓷砖1

3.4.1(b) 欧纳博物馆：瓷砖1
几何画板及绘图内容加载中，请稍等……
2023-03-22 21:29
解析几何变换几何作图
所属专题 geometriadinamica.es
该范例演示了如何使用GeoGebra绘制3.4.1(b)欧纳博物馆瓷砖1。涉及的核心数学概念包括线性方程、对称性和有理数。通过使用Line, Point, OrthogonalLine, Intersect, Midpoint, Mirror, Min, Vector等命令，可以构造出复杂的几何图形。适合高中数学教学和学习。

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(D_1, I) → R_1
  43. Midpoint(I, C_1) → S_1
  44. Midpoint(C_1, E) → T_1
  45. Mirror(F_1, h) → U_1
  46. Mirror(L_1, h) → V_1
  47. Mirror(M_1, h) → W_1
  48. Mirror(T_1, h) → Z_1
  49. Mirror(B_1, h) → A_2
  50. Line(Q, A_2) → d
  51. Line(F, d) → i
  52. Line(C_1, d) → k
  53. Line(S_1, k) → l
  54. Line(R_1, L_1) → j
  55. Line(D_1, j) → m
  56. Line(M, j) → n
  57. Line(I, j) → p
  58. Line(S, A_1) → t
  59. Line(I, T) → a_1
  60. Line(U, B_1) → b_1
  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. Point(a_1) → F_2
  66. Mirror(F_2, m) → L_2
  67. Mirror(F_2, m) → M_2
  68. Point(b) → A1
  69. Min(90, ((a - 1) * 90)) → r1
  70. Line(G_1, O_1) → l_1
  71. OrthogonalLine(G_1, l_1) → m_1
  72. OrthogonalLine(J_1, l_1) → q_1
  73. OrthogonalLine(O_1, l_1) → r_1
  74. OrthogonalLine(R_1, l_1) → s_1
  75. OrthogonalLine(E_1, m_1) → t_1
  76. OrthogonalLine(F_1, m_1) → a_2
  77. Point(a_1) → C
  78. OrthogonalLine(F_2, d) → i_1
  79. OrthogonalLine(C, d) → j_1
  80. Min(180, ((a - 1) * 180)) → r2
  81. Min(270, ((a - 1) * 270)) → r3
  82. Min(180, ((a - 5.5) * 180)) → r4
  83. Midpoint(H_1, G_1) → B_2
  84. Midpoint(G_1, E_1) → C_2
  85. Midpoint(E_1, F_1) → D_2
  86. Midpoint(F_1, U_1) → E_2
  87. Midpoint(O, U) → G_2
  88. Midpoint(U, T) → H_2
  89. Midpoint(T, S) → I_2
  90. Midpoint(S, R) → J_2
  91. Midpoint(I_1, J_1) → K_2
  92. Midpoint(J_1, K_1) → N_2
  93. Midpoint(K_1, L_1) → O_2
  94. Midpoint(L_1, V_1) → P_2
  95. Midpoint(F, N) → Q_2
  96. Midpoint(N, L) → R_2
  97. Midpoint(L, M) → S_2
  98. Midpoint(M, K) → T_2
  99. Midpoint(P_1, O_1) → U_2
  100. Midpoint(O_1, N_1) → V_2
  101. Midpoint(N_1, M_1) → W_2
  102. Midpoint(M_1, W_1) → Z_2
  103. Midpoint(V, C_1) → A_3
  104. Midpoint(C_1, Z) → B_3
  105. Midpoint(Z, D_1) → C_3
  106. Midpoint(D_1, W) → D_3
  107. Mirror(pic1, D_3) → pic1'
  108. Mirror(pic1', T_2) → pic1''
  109. Mirror(pic1'', J_2) → pic1'''
  110. Mirror(J_2, H_1) → E_3
  111. Mirror(U_2, D_1) → F_3
  112. Mirror(V_2, Z) → G_3
  113. Mirror(W_2, C_1) → H_3
  114. Mirror(Z_2, V) → I_3
  115. Mirror(pic1''', E_3) → pic2
  116. Mirror(pic1, F_3) → pic1'_1
  117. Mirror(pic1'_1, G_3) → pic3
  118. Mirror(pic3, H_3) → pic3'
  119. Mirror(pic3', I_3) → pic3''
  120. Mirror(pic1'_1, C_3) → pic4
  121. Mirror(pic4, S_2) → pic4'
  122. Mirror(pic4', I_2) → pic4''
  123. Mirror(pic4'', C_2) → pic4'''
  124. Mirror(pic4', N_2) → pic4''_1
  125. Mirror(pic4, V_2) → pic4'_1
  126. Mirror(pic4'_1, W_2) → pic5
  127. Mirror(pic5, Z_2) → pic5'
  128. Mirror(pic4''_1, O_2) → pic6
  129. Mirror(pic6, P_2) → pic6'
  130. Mirror(pic4''', D_2) → pic7
  131. Mirror(pic7, E_2) → pic7'
  132. Mirror(B_2, Q) → J_3
  133. Mirror(pic2, J_3) → pic2'
  134. Mirror(H_2, E_1) → K_3
  135. Mirror(G_2, F_1) → L_3
  136. Mirror(L_3, J) → M_3
  137. Mirror(pic7', M_3) → pic7''
  138. Mirror(pic7, L_3) → pic7'_1
  139. Mirror(pic4''', K_3) → pic8
  140. Midpoint(E_3, K_3) → Q_1
  141. Vector(K_2, V_2) → u
  142. Vector(K_2, C_2) → w

AI 绘图提示语参考

画一个几何图形，首先绘制一条线段，然后在线段上创建点，并基于这些点构建两条垂直于该线段的线。接着，找到这些线的交点，并计算多个中点。利用中点连接形成新的线段，并通过对称操作（如镜像）生成复杂的几何图案。最终图形应展示出由直线和中点构成的对称结构，体现线性方程、对称性和有理数等数学概念。
以上提示语为根据原始绘图命令整理而来，仅供参考。