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心率数据的分布与相关性探究：不等式约束的几何可视化

心率数据的分布与相关性探究：不等式约束的几何可视化
几何画板及绘图内容加载中，请稍等……
2021-04-12 20:18
圆数列概率统计不等式几何作图
该范例用于演示在“心率（Heart Rates）”数据情境下，如何用图形方式理解数据分布特征、分数化表达与变量间相关关系，并用不等式进行条件约束。 核心数学概念包括：概率统计中的分布与相关性（Correlation），以及代数层面的分数（Fractions）与不等式（Inequalities），必要时结合圆（circumcircle/circumscribed circle）或几何构造来形成直观的几何映射。 作图要点与构造摘要对应：它使用 Sequence 生成数据/样本点序列；If 与 Defined 用于基于条件的判断与对象是否有效的控制；Textfield 用于交互式输入参数（如心率或阈值）；Join、Append 用于把线段/点/文字信息组合成结构化对象并逐步累积；Shuffle 用于对数据或样本进行随机重排以观察分布与相关性变化；还包含 Segment 用于画出关键几何连线；对象体系围绕 studentinput 以及多名学生样本（student1～student33，A、l7、I1、a、text1 等）组织。 适合学段：初高中数学与信息学阶段，作为概率统计、相关性与数据建模入门/复习活动的 GeoGebra 课堂演示或探索作业；也适合数学竞赛前的统计可视化训练。

GeoGebra 命令及参数

  1. Sequence((7.4, (-k)), k, -5.65, 5.39375 - 4.65 / 8, 4.65 / 8) → l7
  2. If(studentinput ≥ 2 ∧ studentinput ≤ 100, studentinput) → students
  3. Textfield(student1) → I1
  4. Defined(students) → a
  5. Textfield(student2) → I2
  6. Textfield(student10) → I10
  7. Textfield(student100) → InputBox102
  8. Textfield(student11) → I11
  9. Textfield(student12) → I12
  10. Textfield(student13) → I13
  11. Textfield(student14) → I14
  12. Textfield(student15) → I15
  13. Textfield(student16) → I16
  14. Textfield(student17) → I17
  15. Textfield(student18) → I18
  16. Textfield(student19) → I19
  17. Textfield(student20) → I20
  18. Textfield(student21) → InputBox16
  19. Textfield(student22) → InputBox17
  20. Textfield(student23) → InputBox18
  21. Textfield(student24) → InputBox19
  22. Textfield(student25) → InputBox20
  23. Textfield(student26) → InputBox21
  24. Textfield(student27) → InputBox22
  25. Textfield(student28) → InputBox23
  26. Textfield(student29) → InputBox24
  27. Textfield(student30) → InputBox25
  28. Textfield(student3) → I3
  29. Textfield(student31) → InputBox27
  30. Textfield(student32) → InputBox28
  31. Textfield(student33) → InputBox29
  32. Textfield(student34) → InputBox30
  33. Textfield(student35) → InputBox31
  34. Textfield(student36) → InputBox32
  35. Textfield(student37) → InputBox33
  36. Textfield(student38) → InputBox34
  37. Textfield(student39) → InputBox35
  38. Textfield(student4) → I4
  39. Textfield(student40) → InputBox37
  40. Textfield(student41) → InputBox38
  41. Textfield(student42) → InputBox39
  42. Textfield(student43) → InputBox40
  43. Textfield(student44) → InputBox41
  44. Textfield(student45) → InputBox42
  45. Textfield(student46) → InputBox43
  46. Textfield(student47) → InputBox44
  47. Textfield(student48) → InputBox45
  48. Textfield(student49) → InputBox46
  49. Textfield(student50) → InputBox47
  50. Textfield(student5) → I5
  51. Textfield(student51) → InputBox49
  52. Textfield(student52) → InputBox50
  53. Textfield(student53) → InputBox51
  54. Textfield(student54) → InputBox52
  55. Textfield(student55) → InputBox53
  56. Textfield(student56) → InputBox54
  57. Textfield(student57) → InputBox55
  58. Textfield(student58) → InputBox56
  59. Textfield(student59) → InputBox57
  60. Textfield(student60) → InputBox58
  61. Textfield(student6) → I6
  62. Textfield(student61) → InputBox60
  63. Textfield(student62) → InputBox61
  64. Textfield(student63) → InputBox62
  65. Textfield(student64) → InputBox63
  66. Textfield(student65) → InputBox64
  67. Textfield(student66) → InputBox65
  68. Textfield(student67) → InputBox66
  69. Textfield(student68) → InputBox67
  70. Textfield(student69) → InputBox68
  71. Textfield(student70) → InputBox70
  72. Textfield(student71) → InputBox71
  73. Textfield(student72) → InputBox72
  74. Textfield(student73) → InputBox73
  75. Textfield(student74) → InputBox74
  76. Textfield(student75) → InputBox75
  77. Textfield(student76) → InputBox76
  78. Textfield(student77) → InputBox77
  79. Textfield(student78) → InputBox78
  80. Textfield(student79) → InputBox79
  81. Textfield(student8) → I8
  82. Textfield(student80) → InputBox81
  83. Textfield(student81) → InputBox82
  84. Textfield(student82) → InputBox83
  85. Textfield(student83) → InputBox84
  86. Textfield(student84) → InputBox85
  87. Textfield(student85) → InputBox86
  88. Textfield(student86) → InputBox87
  89. Textfield(student7) → I7
  90. Textfield(student87) → InputBox88
  91. Textfield(student88) → InputBox89
  92. Textfield(student89) → InputBox90
  93. Textfield(student9) → I9
  94. Textfield(student90) → InputBox92
  95. Textfield(student91) → InputBox93
  96. Textfield(student92) → InputBox94
  97. Textfield(student93) → InputBox95
  98. Textfield(student94) → InputBox96
  99. Textfield(student95) → InputBox97
  100. Textfield(student96) → InputBox98
  101. Textfield(student97) → InputBox99
  102. Textfield(student98) → InputBox100
  103. Textfield(student99) → InputBox101
  104. Sequence((-4.4, (-k)), k, -5.65, -1, 4.65 / 8) → l1
  105. Sequence((-4.55, (-k)), k, -1 + 4.65 / 8, 5.39375, 4.65 / 8) → l2
  106. Sequence((-1.6, (-k)), k, -5.65, 5.39375, 4.65 / 8) → l3
  107. Join({l1, l2}) → l1l2
  108. Sequence((1.35, (-k)), k, -5.65, 5.39375, 4.65 / 8) → l4
  109. Sequence((4.3, (-k)), k, -5.65, 5.39375, 4.65 / 8) → l5
  110. Append(l7, A) → l6
  111. Textfield(studentinput) → InputBox1_{1}
  112. Sequence(Defined[studentvalues(k)], k, 1, 100, 1) → defined
  113. Sequence(studentvalues(k), k, 1, students, 1) → studentvaluesexact
  114. Sequence(k, k, -3.5, 0.5, 1) → xValues1
  115. Sequence((xValues1, (-k)), k, -2.5, 4.7, 0.8) → points1
  116. Sequence(k, k, 5.5, 9.5, 1) → xValues2
  117. Sequence((xValues2, (-k)), k, -2.5, 4.7, 0.8) → points2
  118. Join(points1) → pointsa
  119. Join(points2) → pointsb
  120. Shuffle(pointsa) → pointsaShuffled, {(-1.5, 0.8999999999999999), (-2.5, 2.5), (-0.5, -3.1000000000000005), (-1.5, 0.09999999999999987), (-3.5, 1.7), (-3.5, 0.8999999999999999), (-0.5, -3.9000000000000004), (-2.5, -1.5000000000000002), (-1.5, 1.7), (-1.5, -3.1000000000000005), (-0.5, -4.7), (-3.5, -3.1000000000000005), (0.5, -3.9000000000000004), (-0.5, 2.5), (-1.5, -3.9000000000000004), (-3.5, -2.3000000000000003), (0.5, -3.1000000000000005), (-3.5, 0.09999999999999987), (-2.5, -3.1000000000000005), (-1.5, -0.7000000000000002), (-2.5, -0.7000000000000002), (-3.5, -0.7000000000000002), (0.5, -1.5000000000000002), (0.5, 2.5), (-0.5, -0.7000000000000002), (-0.5, 1.7), (-2.5, -3.9000000000000004), (-3.5, -4.7), (0.5, -2.3000000000000003), (-3.5, 2.5), (-1.5, 2.5), (-0.5, 0.09999999999999987), (0.5, 1.7), (-0.5, 0.8999999999999999), (0.5, 0.09999999999999987), (-1.5, -4.7), (-1.5, -1.5000000000000002), (-3.5, -1.5000000000000002), (0.5, 0.8999999999999999), (-2.5, -4.7), (-2.5, -2.3000000000000003), (-2.5, 0.8999999999999999), (0.5, -0.7000000000000002), (-3.5, -3.9000000000000004), (-2.5, 0.09999999999999987), (-0.5, -1.5000000000000002), (-2.5, 1.7), (0.5, -4.7), (-0.5, -2.3000000000000003), (-1.5, -2.3000000000000003)}
  121. Shuffle(pointsb) → pointsbShuffled, {(8.5, -0.7000000000000002), (8.5, -2.3000000000000003), (8.5, 1.7), (5.5, -4.7), (9.5, -3.1000000000000005), (9.5, -1.5000000000000002), (6.5, 0.09999999999999987), (9.5, -3.9000000000000004), (8.5, -3.1000000000000005), (7.5, -3.1000000000000005), (9.5, 0.8999999999999999), (5.5, -2.3000000000000003), (5.5, 0.8999999999999999), (7.5, -1.5000000000000002), (8.5, -3.9000000000000004), (6.5, -2.3000000000000003), (6.5, 2.5), (9.5, 1.7), (8.5, 0.8999999999999999), (7.5, 1.7), (5.5, 0.09999999999999987), (7.5, -0.7000000000000002), (5.5, -0.7000000000000002), (5.5, 1.7), (5.5, -3.9000000000000004), (9.5, -4.7), (5.5, -1.5000000000000002), (9.5, -2.3000000000000003), (6.5, -1.5000000000000002), (6.5, -0.7000000000000002), (6.5, 0.8999999999999999), (8.5, -1.5000000000000002), (9.5, 2.5), (8.5, 0.09999999999999987), (6.5, -3.1000000000000005), (6.5, -3.9000000000000004), (6.5, 1.7), (9.5, -0.7000000000000002), (6.5, -4.7), (8.5, 2.5), (5.5, 2.5), (7.5, -3.9000000000000004), (7.5, 0.8999999999999999), (7.5, -2.3000000000000003), (7.5, 2.5), (8.5, -4.7), (7.5, -4.7), (9.5, 0.09999999999999987), (5.5, -3.1000000000000005), (7.5, 0.09999999999999987)}
  122. Segment(F, G) → f

AI 绘图提示语参考

创建一个动态图形，展示心率数据分布与不等式约束的关系。首先生成一个序列表示心率数据，然后根据用户输入筛选出有效数据。使用文本框显示多个学生样本数据，并通过条件判断处理数据有效性。利用连接线段展示数据间的关系，并应用不等式条件作为约束，最终形成一个包含概率统计、分数表示和几何构造的综合可视化模型，适合数据分析教学演示。
以上提示语为根据原始绘图命令整理而来，仅供参考。