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差数模型：立方体、条块与数字的随机排列可视化

差数模型：立方体、条块与数字的随机排列可视化
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2020-10-03 02:19
数列立体几何概率统计几何作图函数图像
本范例演示一种基于差值（Difference Numbers）思想的数字模型，通过随机过程生成不同的数字表示形式。核心数学概念包括：随机过程（Random命令生成随机数）、2D向量（Vectors 2D）的表示、以及几何对象的变换与排列。作图要点：利用Sequence命令生成序列，Point命令创建关键点，Random命令实现随机数字生成，RotateText命令旋转文本标签，Ellipse绘制椭圆，Polygon构建多边形，Segment绘制线段，Textfield创建交互文本框；对象包括多个坐标点（A、B、E、F、I、J、M、N、Q、R及其下标变体）、列表对象（list24、list25）以及文本框控件（text1-text6）和按钮（button1）。该模型适合小学至初中数学教学，可用于帮助学生理解数字的位值概念（个位、十位、百位）、随机事件的概率意义，以及通过几何直观感受数学规律。

GeoGebra 命令及参数

  1. Sequence((i, 23), i, 70, 88, 2) → list24
  2. Point(list24) → A
  3. Point(list24) → B
  4. Point(list24) → E
  5. Point(list24) → F
  6. Point(list24) → I
  7. Point(list24) → J
  8. Point(list24) → M
  9. Point(list24) → N
  10. Point(list24) → Q
  11. Point(list24) → R
  12. Sequence((i, 27), i, 70, 88, 2) → list25
  13. Point(list25) → U
  14. Point(list25) → V
  15. Point(list25) → A_1
  16. Point(list25) → B_1
  17. Point(list25) → E_1
  18. Point(list25) → F_1
  19. Point(list25) → I_1
  20. Point(list25) → J_1
  21. Point(list25) → M_1
  22. Point(list25) → N_1
  23. Point(list25) → Q_1
  24. Point(list25) → R_1
  25. Point(list24) → U_1
  26. Point(list24) → V_1
  27. Random(1, 9) → rhund
  28. Random(0, 9) → rten
  29. Random(0, 9) → rone
  30. RotateText(text4, 45°) → text10
  31. RotateText(text5, 45°) → text11
  32. RotateText(text6, 45°) → text12
  33. Ellipse(A_2, B_2, C_2) → c_2
  34. Polygon(D_2, E_2, F_2, G_2) → poly13, d_2, e_2, f_3, g_3
  35. Point(g_3) → H_2
  36. Point(e_2) → I_2
  37. Segment(H_2, I_2) → q_2
  38. Textfield(YourGuess) → InputBox1
  39. RotateText(text17, 45°) → text18
  40. Point(list25) → C
  41. Point(list25) → D
  42. Polygon(C, D, 4) → poly1, f, g, h, i, G, H
  43. Point(list25) → K
  44. Point(list25) → L
  45. Polygon(K, L, 4) → poly2, j, k, l, m, O, P
  46. Point(list25) → S
  47. Point(list25) → T
  48. Polygon(T, S, 4) → poly3, n, p, q, r, W, Z
  49. Point(list25) → C_1
  50. Point(list25) → D_1
  51. Polygon(D_1, C_1, 4) → poly4, s, t, a, b, G_1, H_1
  52. Point(list25) → K_1
  53. Point(list25) → L_1
  54. Polygon(K_1, L_1, 4) → poly5, c, d, e, f_1, O_1, P_1
  55. Point(list24) → S_1
  56. Point(list24) → T_1
  57. Polygon(T_1, S_1, 4) → poly6, g_1, h_1, i_1, j_1, W_1, Z_1
  58. Point(list24) → J_2
  59. Point(list24) → K_2
  60. Polygon(J_2, K_2, 4) → poly7, k_1, l_1, m_1, n_1, L_2, M_2
  61. Point(list24) → N_2
  62. Point(list24) → O_2
  63. Polygon(N_2, O_2, 4) → poly8, p_1, q_1, r_1, s_1, P_2, Q_2
  64. Point(list24) → R_2
  65. Point(list24) → S_2
  66. Polygon(R_2, S_2, 4) → poly9, t_1, a_1, b_1, c_1, T_2, U_2
  67. Point(list24) → V_2
  68. Point(list24) → W_2
  69. Polygon(V_2, W_2, 4) → poly10, d_1, e_1, f_2, g_2, Z_2, A_3
  70. Sequence(Polygon[(68, i), (68, i + 1), 4], i, 22, 31) → list15
  71. Sequence(Polygon[(68, i), (68, i + 1), 4], i, 11, 20) → list19
  72. Sequence(Polygon[(68, i), (68, i + 1), 4], i, 0, 9) → list14
  73. Sequence(Polygon[(66, i), (66, i + 1), 4], i, 0, 9) → list13
  74. Sequence(Polygon[(66, i), (66, i + 1), 4], i, 11, 20) → list20
  75. Sequence(Polygon[(66, i), (66, i + 1), 4], i, 22, 31) → list17
  76. Sequence(Polygon[(64, i), (64, i + 1), 4], i, 22, 31) → list18
  77. Sequence(Polygon[(64, i), (64, i + 1), 4], i, 11, 20) → list21
  78. Sequence(Polygon[(64, i), (64, i + 1), 4], i, 0, 9) → list12
  79. Sequence(Sequence[Polygon[(j, i), (j, i + 1), 4], i, 22, 31], j, 53, 62) → list11
  80. Sequence(Sequence[Polygon[(j, i), (j, i + 1), 4], i, 11, 20], j, 53, 62) → list8
  81. Sequence(Sequence[Polygon[(j, i), (j, i + 1), 4], i, 0, 9], j, 53, 62) → list6
  82. Sequence(Sequence[Polygon[(j, i), (j, i + 1), 4], i, 22, 31], j, 42, 51) → list10
  83. Sequence(Sequence[Polygon[(j, i), (j, i + 1), 4], i, 11, 20], j, 42, 51) → list4
  84. Sequence(Sequence[Polygon[(j, i), (j, i + 1), 4], i, 0, 9], j, 42, 51) → list5
  85. Sequence(Sequence[Polygon[(j, i), (j, i + 1), 4], i, 0, 9], j, 31, 40) → list1
  86. Sequence(Sequence[Polygon[(j, i), (j, i + 1), 4], i, 11, 20], j, 31, 40) → list2
  87. Sequence(Sequence[Polygon[(j, i), (j, i + 1), 4], i, 22, 31], j, 31, 40) → list3
  88. Sequence(Sequence[Polygon[(i, j), (i + 4, j), 4], i, 69, 87, 4], j, 22, 26, 4) → list23

AI 绘图提示语参考

这是一个基于差值数的随机可视化模型，包含多个点、序列和随机生成的数字。点A、B、E、F、I、J、M、N、Q、R和U、V、A_1、B_1等代表不同的数值。随机命令生成随机数字，用于旋转文本和绘制椭圆、线段和三角形。模型帮助学生理解数位概念和概率意义，通过几何表示直观展示数学模式。
以上提示语为根据原始绘图命令整理而来，仅供参考。