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怪物分布

怪物分布
几何画板及绘图内容加载中，请稍等……
2018-11-29 08:31
立体几何概率统计最值优化几何作图
①本范例演示了在三维空间中生成多个怪物并计算它们与特定平面的交点数量；②涉及的核心数学概念包括假设检验、曲面、线性规划、极限和概率统计；③作图要点提炼自构造摘要，使用了Intersect（交集）、Polygon（多边形）、Circle（圆）、CountIf（计数）、Midpoint（中点）、Vector（向量）、Translate（平移）、If（条件判断）等GeoGebra命令和对象；④适合高中及以上数学学习者，用于理解空间几何与概率统计的结合应用。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → C_2
  2. Polygon(C_2, C_1, 10) → poly1, f, p, C_{10}, C_{9}, C_8, C_7, C_6, C_5, C_4, C_3, g, h, i, j, k, l, m, n
  3. Circle(C_6, 0.4) → e_6
  4. CountIf(IsInRegion[T, e_6], T, {C_1M3, C_2M3, C_3M3}) → count_{e6}M3
  5. CountIf(IsInRegion[T, e_6], T, {C_1M1, C_2M1, C_3M1, C_4M1}) → count_{e6}M1
  6. CountIf(IsInRegion[T, e_6], T, {C_1M2, C_2M2, C_3M2}) → count_{e6}M2
  7. Circle(C_{10}, 0.4) → e_x
  8. CountIf(IsInRegion[T, e_x], T, {C_1M1, C_2M1, C_3M1, C_4M1}) → count_{ex}M1
  9. CountIf(IsInRegion[T, e_x], T, {C_1M2, C_2M2, C_3M2}) → count_{ex}M2
  10. CountIf(IsInRegion[T, e_x], T, {C_1M3, C_2M3, C_3M3}) → count_{ex}M3
  11. Circle(C_{9}, 0.4) → e_9
  12. CountIf(IsInRegion[T, e_9], T, {C_1M1, C_2M1, C_3M1, C_4M1}) → count_{e9}M1
  13. CountIf(IsInRegion[T, e_9], T, {C_1M3, C_2M3, C_3M3}) → count_{e9}M3
  14. CountIf(IsInRegion[T, e_9], T, {C_1M2, C_2M2, C_3M2}) → count_{e9}M2
  15. Circle(C_8, 0.4) → e_8
  16. CountIf(IsInRegion[T, e_8], T, {C_1M1, C_2M1, C_3M1, C_4M1}) → count_{e8}M1
  17. CountIf(IsInRegion[T, e_8], T, {C_1M3, C_2M3, C_3M3}) → count_{e8}M3
  18. CountIf(IsInRegion[T, e_8], T, {C_1M2, C_2M2, C_3M2}) → count_{e8}M2
  19. Circle(C_3, 0.4) → e_3
  20. CountIf(IsInRegion[T, e_3], T, {C_1M1, C_2M1, C_3M1, C_4M1}) → count_{e3}M1
  21. CountIf(IsInRegion[T, e_3], T, {C_1M3, C_2M3, C_3M3}) → count_{e3}M3
  22. CountIf(IsInRegion[T, e_3], T, {C_1M2, C_2M2, C_3M2}) → count_{e3}M2
  23. Circle(C_4, 0.4) → e_4
  24. CountIf(IsInRegion[T, e_4], T, {C_1M1, C_2M1, C_3M1, C_4M1}) → count_{e4}M1
  25. CountIf(IsInRegion[T, e_4], T, {C_1M3, C_2M3, C_3M3}) → count_{e4}M3
  26. CountIf(IsInRegion[T, e_4], T, {C_1M2, C_2M2, C_3M2}) → count_{e4}M2
  27. Circle(C_5, 0.4) → e_5
  28. CountIf(IsInRegion[T, e_5], T, {C_1M1, C_2M1, C_3M1, C_4M1}) → count_{e5}M1
  29. CountIf(IsInRegion[T, e_5], T, {C_1M3, C_2M3, C_3M3}) → count_{e5}M3
  30. CountIf(IsInRegion[T, e_5], T, {C_1M2, C_2M2, C_3M2}) → count_{e5}M2
  31. Circle(C_7, 0.4) → e_7
  32. CountIf(IsInRegion[T, e_7], T, {C_1M1, C_2M1, C_3M1, C_4M1}) → count_{e7}M1
  33. CountIf(IsInRegion[T, e_7], T, {C_1M3, C_2M3, C_3M3}) → count_{e7}M3
  34. CountIf(IsInRegion[T, e_7], T, {C_1M2, C_2M2, C_3M2}) → count_{e7}M2
  35. Circle(C_2, 0.4) → e_2
  36. CountIf(IsInRegion[T, e_2], T, {C_1M1, C_2M1, C_3M1, C_4M1}) → count_{e2}M1
  37. CountIf(IsInRegion[T, e_2], T, {C_1M2, C_2M2, C_3M2}) → count_{e2}M2
  38. CountIf(IsInRegion[T, e_2], T, {C_1M3, C_2M3, C_3M3}) → count_{e2}M3
  39. Circle(C_1, 0.4) → e_1
  40. CountIf(IsInRegion[T, e_1], T, {C_1M2, C_2M2, C_3M2}) → count_{e1}M2
  41. CountIf(IsInRegion[T, e_1], T, {C_1M3, C_2M3, C_3M3}) → count_{e1}M3
  42. CountIf(IsInRegion[T, e_1], T, {C_1M1, C_2M1, C_3M1, C_4M1}) → count_{e1}M1
  43. Circle(C_1, 1.5) → c_1
  44. Circle(C_2, 1.5) → c_2
  45. Circle(C_3, 1.5) → c_3
  46. Circle(C_4, 1.5) → c_4
  47. Circle(C_5, 1.5) → c_5
  48. Circle(C_6, 1.5) → c_6
  49. Circle(C_7, 1.5) → c_7
  50. Circle(C_8, 1.5) → c_8
  51. Circle(C_{9}, 1.5) → c_9
  52. Circle(C_{10}, 1.5) → c_{10}
  53. Circle(C_5, 1.5) → d_5
  54. Circle(C_6, 1.5) → d_6
  55. Circle(C_7, 1.5) → d_7
  56. Circle(C_8, 1.5) → d_8
  57. Circle(C_{9}, 1.5) → d_9
  58. Circle(C_{10}, 1.5) → d_{10}
  59. Circle(C_1, 1.5) → d_1
  60. Circle(C_2, 1.5) → d_2
  61. Circle(C_3, 1.5) → d_3
  62. Circle(C_4, 1.5) → d_4
  63. Polygon(Q_1, Q_2, 4) → poly2, q, r, s, t, Q_3, Q_4
  64. Midpoint(Q_4, Q_2) → Q_0
  65. Vector(Q_0, Q_1) → u
  66. Translate(C_2, u) → A_2
  67. Translate(C_3, u) → A_3
  68. Translate(C_4, u) → A_4
  69. Translate(C_5, u) → A_5
  70. Translate(C_6, u) → A_6
  71. Translate(C_7, u) → A_7
  72. Translate(C_8, u) → A_8
  73. Translate(C_{9}, u) → A_9
  74. Translate(C_{10}, u) → A_{10}
  75. Translate(C_1, u) → A_1
  76. If(count_{e1}M1 ≟ 1 ∧ count_{e1}M2 ≟ 0 ∧ count_{e1}M3 ≟ 0, 1, If[count_{e1}M1 ≟ 0 ∧ count_{e1}M2 ≟ 1 ∧ count_{e1}M3 ≟ 0, 2, If[count_{e1}M1 ≟ 0 ∧ count_{e1}M2 ≟ 0 ∧ count_{e1}M3 ≟ 1, 3, 0]]) → n_1
  77. If(count_{e2}M1 ≟ 1 ∧ count_{e2}M2 ≟ 0 ∧ count_{e2}M3 ≟ 0, 1, If[count_{e2}M1 ≟ 0 ∧ count_{e2}M2 ≟ 1 ∧ count_{e2}M3 ≟ 0, 2, If[count_{e2}M1 ≟ 0 ∧ count_{e2}M2 ≟ 0 ∧ count_{e2}M3 ≟ 1, 3, 0]]) → n_2
  78. If(count_{e3}M1 ≟ 1 ∧ count_{e3}M2 ≟ 0 ∧ count_{e3}M3 ≟ 0, 1, If[count_{e3}M1 ≟ 0 ∧ count_{e3}M2 ≟ 1 ∧ count_{e3}M3 ≟ 0, 2, If[count_{e3}M1 ≟ 0 ∧ count_{e3}M2 ≟ 0 ∧ count_{e3}M3 ≟ 1, 3, 0]]) → n_3
  79. If(count_{e4}M1 ≟ 1 ∧ count_{e4}M2 ≟ 0 ∧ count_{e4}M3 ≟ 0, 1, If[count_{e4}M1 ≟ 0 ∧ count_{e4}M2 ≟ 1 ∧ count_{e4}M3 ≟ 0, 2, If[count_{e4}M1 ≟ 0 ∧ count_{e4}M2 ≟ 0 ∧ count_{e4}M3 ≟ 1, 3, 0]]) → n_4
  80. If(count_{e5}M1 ≟ 1 ∧ count_{e5}M2 ≟ 0 ∧ count_{e5}M3 ≟ 0, 1, If[count_{e5}M1 ≟ 0 ∧ count_{e5}M2 ≟ 1 ∧ count_{e5}M3 ≟ 0, 2, If[count_{e5}M1 ≟ 0 ∧ count_{e5}M2 ≟ 0 ∧ count_{e5}M3 ≟ 1, 3, 0]]) → n_5
  81. If(count_{e6}M1 ≟ 1 ∧ count_{e6}M2 ≟ 0 ∧ count_{e6}M3 ≟ 0, 1, If[count_{e6}M1 ≟ 0 ∧ count_{e6}M2 ≟ 1 ∧ count_{e6}M3 ≟ 0, 2, If[count_{e6}M1 ≟ 0 ∧ count_{e6}M2 ≟ 0 ∧ count_{e6}M3 ≟ 1, 3, 0]]) → n_6
  82. If(count_{e7}M1 ≟ 1 ∧ count_{e7}M2 ≟ 0 ∧ count_{e7}M3 ≟ 0, 1, If[count_{e7}M1 ≟ 0 ∧ count_{e7}M2 ≟ 1 ∧ count_{e7}M3 ≟ 0, 2, If[count_{e7}M1 ≟ 0 ∧ count_{e7}M2 ≟ 0 ∧ count_{e7}M3 ≟ 1, 3, 0]]) → n_7
  83. If(count_{e8}M1 ≟ 1 ∧ count_{e8}M2 ≟ 0 ∧ count_{e8}M3 ≟ 0, 1, If[count_{e8}M1 ≟ 0 ∧ count_{e8}M2 ≟ 1 ∧ count_{e8}M3 ≟ 0, 2, If[count_{e8}M1 ≟ 0 ∧ count_{e8}M2 ≟ 0 ∧ count_{e8}M3 ≟ 1, 3, 0]]) → n_8
  84. If(count_{e9}M1 ≟ 1 ∧ count_{e9}M2 ≟ 0 ∧ count_{e9}M3 ≟ 0, 1, If[count_{e9}M1 ≟ 0 ∧ count_{e9}M2 ≟ 1 ∧ count_{e9}M3 ≟ 0, 2, If[count_{e9}M1 ≟ 0 ∧ count_{e9}M2 ≟ 0 ∧ count_{e9}M3 ≟ 1, 3, 0]]) → n_9
  85. If(count_{ex}M1 ≟ 1 ∧ count_{ex}M2 ≟ 0 ∧ count_{ex}M3 ≟ 0, 1, If[count_{ex}M1 ≟ 0 ∧ count_{ex}M2 ≟ 1 ∧ count_{ex}M3 ≟ 0, 2, If[count_{ex}M1 ≟ 0 ∧ count_{ex}M2 ≟ 0 ∧ count_{ex}M3 ≟ 1, 3, 0]]) → n_{10}
  86. CountIf(T ≟ 1, T, alln) → contandoM_1
  87. CountIf(T ≟ 2, T, alln) → contandoM_2
  88. CountIf(T ≟ 3, T, alln) → contandoM_3
  89. Translate(C_1M1, w) → C_1M1'
  90. Translate(C_1M1', v) → C_1M1''
  91. Circle(C_1M1, 1.2) → c_{1M1}
  92. Translate(C_2M1, w) → C_2M1'
  93. Translate(C_2M1', v) → C_2M1''
  94. Circle(C_2M1, 1.2) → c_{2M1}
  95. Translate(C_3M1, w) → C_3M1'
  96. Translate(C_4M1, w) → C_4M1'
  97. Translate(C_3M1', v) → C_3M1''
  98. Translate(C_4M1', v) → C_4M1''
  99. Circle(C_3M1, 1.2) → c_{3M1}
  100. Circle(C_4M1, 1.2) → c_{4M1}
  101. Translate(C_1M2, w) → C_1M2'
  102. Translate(C_2M2, w) → C_2M2'
  103. Translate(C_3M2, w) → C_3M2'
  104. Translate(C_1M2', v) → C_1M2''
  105. Translate(C_2M2', v) → C_2M2''
  106. Translate(C_3M2', v) → C_3M2''
  107. Circle(C_1M2, 1.2) → c_{1M2}
  108. Circle(C_2M2, 1.2) → c_{2M2}
  109. Circle(C_3M2, 1.2) → c_{3M2}
  110. Translate(C_1M3, w) → C_1M3'
  111. Translate(C_2M3, w) → C_2M3'
  112. Translate(C_3M3, w) → C_3M3'
  113. Translate(C_1M3', v) → C_1M3''
  114. Translate(C_2M3', v) → C_2M3''
  115. Translate(C_3M3', v) → C_3M3''
  116. Circle(C_1M3, 1.2) → c_{1M3}
  117. Circle(C_2M3, 1.2) → c_{2M3}
  118. Circle(C_3M3, 1.2) → c_{3M3}
  119. If(n_1 ≠ 0 ∧ n_2 ≠ 0 ∧ n_3 ≠ 0 ∧ n_4 ≠ 0 ∧ n_5 ≠ 0 ∧ n_6 ≠ 0 ∧ n_7 ≠ 0 ∧ n_8 ≠ 0 ∧ n_9 ≠ 0 ∧ n_{10} ≠ 0, 1, 0) → all_nnull