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收银机：随机找零与硬币堆叠的几何模拟

收银机：随机找零与硬币堆叠的几何模拟
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2017-03-01 04:19
多边形概率统计几何作图滑块动画
所属专题 Elementary School Applets
① 本范例通过GeoGebra构建一个收银机场景，演示随机生成硬币并堆叠在矩形区域内的动态过程，直观展示随机性与几何形状的交互。② 核心数学概念包括超几何分布（用于模拟从有限硬币中抽取）、随机数生成、多边形构造以及体积（通过硬币堆叠高度体现）和矩形面积计算。③ 作图要点：使用Point定义硬币中心，Polygon构造硬币多边形，Shuffle和RandomElement实现随机抽取，Random控制随机参数，Intersect用于检测碰撞，Element和If处理条件逻辑；对象包括大量点（A, B_4, C_4等）和变量（pennysize, R, S等），通过滑块或随机命令驱动动态变化。④ 适合中学数学或概率统计课程，用于演示随机模拟、几何构造与分布概念，也可作为编程式数学建模的入门案例。

GeoGebra 命令及参数

  1. Point(xAxis) → C_4
  2. pennycenter(R_{11}, pennysize) → T
  3. pennycenter(R_{13}, pennysize) → U
  4. pennycenter(R_{14}, pennysize) → V
  5. pennycenter(R_{15}, pennysize) → W
  6. pennycenter(R_{16}, pennysize) → Z
  7. pennycenter(R_{10}, pennysize) → A_1
  8. pennycenter(R_{17}, pennysize) → B_1
  9. pennycenter(R_{18}, pennysize) → C_1
  10. pennycenter(R_{19}, pennysize) → D_1
  11. pennycenter(R_1, pennysize) → E_1
  12. pennycenter(R_2, pennysize) → F_1
  13. pennycenter(R_3, pennysize) → G_1
  14. pennycenter(R_4, pennysize) → H_1
  15. pennycenter(R_5, pennysize) → I_1
  16. pennycenter(R_6, pennysize) → J_1
  17. pennycenter(R_7, pennysize) → K_1
  18. pennycenter(R_8, pennysize) → L_1
  19. pennycenter(R_9, pennysize) → M_1
  20. pennycenter(R_{12}, pennysize) → N_1
  21. pennycenter(O_1, nickelsize) → Q_1
  22. pennycenter(O_2, nickelsize) → T_1
  23. pennycenter(O_3, nickelsize) → U_1
  24. pennycenter(O_4, nickelsize) → V_1
  25. pennycenter(O_5, nickelsize) → W_1
  26. pennycenter(O_6, nickelsize) → Z_1
  27. pennycenter(O_7, nickelsize) → A_2
  28. pennycenter(O_8, nickelsize) → B_2
  29. pennycenter(O_9, nickelsize) → C_2
  30. pennycenter(O_{10}, nickelsize) → D_2
  31. pennycenter(O_{11}, nickelsize) → E_2
  32. pennycenter(O_{12}, nickelsize) → F_2
  33. pennycenter(O_{13}, nickelsize) → G_2
  34. pennycenter(O_{14}, nickelsize) → H_2
  35. pennycenter(O_{15}, nickelsize) → I_2
  36. pennycenter(O_{16}, nickelsize) → J_2
  37. pennycenter(O_{17}, nickelsize) → K_2
  38. pennycenter(O_{18}, nickelsize) → L_2
  39. pennycenter(O_{19}, nickelsize) → M_2
  40. pennycenter(O_{20}, nickelsize) → N_2
  41. Polygon(J_3, K_3, C_4, D_4, E_4, F_4, G_4, I_3, L_3, M_3, A, V_3, W_3, Z_3, A_4, B_4) → poly4, h, r, s, t, f_1, g_1, h_1, i_1, i, j, k, l, m, n, p, q
  42. pennycenter(E_6, dimesize) → D_6
  43. pennycenter(E_7, dimesize) → F_6
  44. pennycenter(E_8, dimesize) → G_6
  45. pennycenter(E_9, dimesize) → H_6
  46. pennycenter(E_{10}, dimesize) → I_6
  47. pennycenter(E_{11}, dimesize) → J_6
  48. pennycenter(E_{12}, dimesize) → K_6
  49. pennycenter(E_{13}, dimesize) → L_6
  50. pennycenter(E_{14}, dimesize) → M_6
  51. pennycenter(E_{15}, dimesize) → N_6
  52. pennycenter(E_{16}, dimesize) → Q_6
  53. pennycenter(E_{17}, dimesize) → T_6
  54. pennycenter(E_{18}, dimesize) → U_6
  55. pennycenter(E_{19}, dimesize) → V_6
  56. pennycenter(E_{21}, dimesize) → W_6
  57. pennycenter(E_{22}, dimesize) → Z_6
  58. pennycenter(E_{23}, dimesize) → A_7
  59. pennycenter(E_{24}, dimesize) → B_7
  60. pennycenter(E, dimesize) → D_7
  61. pennycenter(E_{20}, dimesize) → F_7
  62. pennycenter(G_7, quartersize) → I_7
  63. pennycenter(G_{10}, quartersize) → J_7
  64. pennycenter(G_9, quartersize) → K_7
  65. pennycenter(G_8, quartersize) → L_7
  66. pennycenter(G_{14}, quartersize) → M_7
  67. pennycenter(G_{13}, quartersize) → N_7
  68. pennycenter(G_{12}, quartersize) → Q_7
  69. pennycenter(G_{11}, quartersize) → T_7
  70. pennycenter(G_{18}, quartersize) → U_7
  71. pennycenter(G_{17}, quartersize) → V_7
  72. pennycenter(G_{16}, quartersize) → W_7
  73. pennycenter(G_{15}, quartersize) → Z_7
  74. pennycenter(G_{19}, quartersize) → A_8
  75. pennycenter(G_{20}, quartersize) → B_8
  76. pennycenter(G_{21}, quartersize) → D_8
  77. pennycenter(G_{22}, quartersize) → F_8
  78. pennycenter(G_{23}, quartersize) → I_8
  79. pennycenter(G_{24}, quartersize) → J_8
  80. pennycenter(G_{25}, quartersize) → K_8
  81. pennycenter(G_{26}, quartersize) → L_8
  82. Shuffle(Remove[Flatten[Sequence[Sequence[Point[{i, j}], i, -32, -22, 3], j, 8, 0, -3]], {(-32, 8), (-23, 2)}]) → leftbanklist
  83. Polygon(C_4, B_4, A_4, Z_3, E_4, D_4) → poly1, c_4, b_4, a_4, z_3, e_4, d_4
  84. Polygon(B, C, D, F) → poly2, b_1, c_1, d_1, f_2
  85. Intersect(z_3, e_4) → J
  86. Polygon(J, F_4, W_3, Z_3) → poly3, j_2, f_4, w_3, z_1
  87. Polygon(F_4, G_4, V_3, W_3) → poly5, f_3, g_4, v_3, w_1
  88. Polygon(G_4, I_3, A, V_3) → poly6, g_2, i_3, a_1, v_1
  89. Polygon(H_4, I_4, N_3, U_3) → poly7, h_4, i_4, n_3, u_3
  90. Polygon(J_3, K_3, L_3, M_3) → poly8, j_3, k_3, l_3, m_3
  91. Polygon(K, L, M, N) → poly9, k_2, l_2, m_2, n_1
  92. Polygon(O, P, Q, Q_2) → poly10, o, p_1, q_1, q_2
  93. RandomElement({"gum", "yo-yo", "bottle of bubbles", "top", "candy", "lollipop", "pencil"}) → buying
  94. Element({"1¢", "10¢", "20¢", "50¢", "$1.00"}, u) → maxText
  95. Random(Element[{1, 10, 20, 50, 100}, u - 1], Element[{1, 10, 20, 50, 100}, u]) → cost
  96. If(cost ≟ 100, "$1.00", Text[cost] + "¢") → costText
  97. If(Rtotal ≟ 0, "0¢", If[Rtotal < 100, Rtotal + "¢", "$" + Rhundreds + "." + Rtens + Rones]) → text2
  98. If(cost ≟ Rtotal, "You bought it!", If[cost > Rtotal, "You haven't paid enough.", "You paid too much."]) → checkText

AI 绘图提示语参考

在一个矩形区域内，随机生成并堆叠不同大小的圆形硬币，展示随机性与几何形状的相互作用。使用随机数生成不同硬币的位置和大小，通过多边形构造硬币形状，并检测硬币之间的碰撞以避免重叠。展示多种硬币（如分币、五分币、一角币）的堆叠效果，并利用滑块控制硬币大小和数量，直观呈现概率分布和几何构造的概念。
以上提示语为根据原始绘图命令整理而来，仅供参考。