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交互式伽尔顿板

交互式伽尔顿板
几何画板及绘图内容加载中，请稍等……
2014-01-07 03:01
概率统计几何作图滑块动画函数图像
所属专题 Statistics and Probability with Mr Downes !Statistics
①本范例演示了伽尔顿板的交互式模型，通过可视化展示小球下落过程中的分布规律。②涉及的核心数学概念包括二项分布、组合数学、条件概率、算术运算及逻辑推理。③作图要点：利用 GeoGebra 命令如 If、Element、RemoveUndefined、Point、Sequence、Take、PolyLine、Segment、Vector、BinomialDist、BarChart、Textfield、Polygon、Sum、TableText、LaTeX 构建图形，实现动态演示。④适合高中及以上学生学习概率统计、离散数学及数据可视化，也可用于教学演示。

GeoGebra 命令及参数

  1. If(J32 ≟ 0, -1, 1) → K32
  2. If(J31 ≟ 0, -1, 1) → K31
  3. If(J30 ≟ 0, -1, 1) → K30
  4. If(J29 ≟ 0, -1, 1) → K29
  5. If(J28 ≟ 0, -1, 1) → K28
  6. If(J27 ≟ 0, -1, 1) → K27
  7. If(J26 ≟ 0, -1, 1) → K26
  8. If(J25 ≟ 0, -1, 1) → K25
  9. If(J24 ≟ 0, -1, 1) → K24
  10. If(J23 ≟ 0, -1, 1) → K23
  11. If(J22 ≟ 0, -1, 1) → K22
  12. If(J3 ≟ 0, -1, 1) → K3
  13. If(J4 ≟ 0, -1, 1) → K4
  14. If(J5 ≟ 0, -1, 1) → K5
  15. If(J6 ≟ 0, -1, 1) → K6
  16. If(J7 ≟ 0, -1, 1) → K7
  17. If(J8 ≟ 0, -1, 1) → K8
  18. If(J9 ≟ 0, -1, 1) → K9
  19. If(J10 ≟ 0, -1, 1) → K10
  20. If(J11 ≟ 0, -1, 1) → K11
  21. If(J12 ≟ 0, -1, 1) → K12
  22. If(J13 ≟ 0, -1, 1) → K13
  23. If(J14 ≟ 0, -1, 1) → K14
  24. If(J15 ≟ 0, -1, 1) → K15
  25. If(J16 ≟ 0, -1, 1) → K16
  26. If(J17 ≟ 0, -1, 1) → K17
  27. If(J18 ≟ 0, -1, 1) → K18
  28. If(J19 ≟ 0, -1, 1) → K19
  29. If(J20 ≟ 0, -1, 1) → K20
  30. If(J21 ≟ 0, -1, 1) → K21
  31. Element(contador1, R33) → S33
  32. Element(contador1, R32) → S32
  33. Element(contador1, R31) → S31
  34. Element(contador1, R30) → S30
  35. Element(contador1, R29) → S29
  36. Element(contador1, R28) → S28
  37. Element(contador1, R27) → S27
  38. Element(contador1, R26) → S26
  39. Element(contador1, R25) → S25
  40. Element(contador1, R24) → S24
  41. Element(contador1, R23) → S23
  42. Element(contador1, R22) → S22
  43. Element(contador1, R21) → S21
  44. Element(contador1, R20) → S20
  45. Element(contador1, R19) → S19
  46. Element(contador1, R18) → S18
  47. Element(contador1, R17) → S17
  48. Element(contador1, R16) → S16
  49. Element(contador1, R15) → S15
  50. Element(contador1, R14) → S14
  51. Element(contador1, R13) → S13
  52. Element(contador1, R12) → S12
  53. Element(contador1, R11) → S11
  54. Element(contador1, R10) → S10
  55. Element(contador1, R9) → S9
  56. Element(contador1, R8) → S8
  57. Element(contador1, R7) → S7
  58. Element(contador1, R6) → S6
  59. Element(contador1, R5) → S5
  60. Element(contador1, R4) → S4
  61. Element(contador1, R3) → S3
  62. Element(contador1, R2) → S2
  63. RemoveUndefined(S2:S33) → Ergebnisliste
  64. Point(yAxis) → A
  65. Sequence(Sequence[(i, (j * h)), i, ((-0.5) * j), 0 + (0.5 * j)], j, 0, len) → Scheitelpunkte
  66. Sequence(Sequence[Polygon[(i, (j * h) + (0.2 * h)), (i - 0.5 + 0.2, ((j + 1) * h) - (0.2 * h)), (i + 0.5 - 0.2, ((j + 1) * h) - (0.2 * h))], i, ((-0.5) * j), 0 + (0.5 * j)], j, 0, len - 1) → Galtonbrett
  67. Take(N1:N32, 1, len + 2) → Weg
  68. PolyLine(Weg) → a
  69. If(e, skal / 2, Max[Ergebnisliste] + 1) → höhe
  70. Segment((((-len) - 1) / 2, y(B)), ((len + 1) / 2, y(B))) → c
  71. Element(Last[Take[N1:N32, 1, len + 2]], 1) → D
  72. Vector(D, (x(D), y(B))) → u
  73. Sequence(len + 1) → Liste2
  74. If(J33 ≟ 0, -1, 1) → K33
  75. BinomialDist(len, p, I5, false) → P5
  76. BinomialDist(len, p, I4, false) → P4
  77. BinomialDist(len, p, I2, false) → P2
  78. BinomialDist(len, p, I3, false) → P3
  79. BinomialDist(len, p, I6, false) → P6
  80. BinomialDist(len, p, I7, false) → P7
  81. BinomialDist(len, p, I8, false) → P8
  82. BinomialDist(len, p, I9, false) → P9
  83. BinomialDist(len, p, I10, false) → P10
  84. BinomialDist(len, p, I11, false) → P11
  85. BinomialDist(len, p, I12, false) → P12
  86. BinomialDist(len, p, I13, false) → P13
  87. BinomialDist(len, p, I14, false) → P14
  88. BinomialDist(len, p, I15, false) → P15
  89. BinomialDist(len, p, I16, false) → P16
  90. BinomialDist(len, p, I17, false) → P17
  91. BinomialDist(len, p, I18, false) → P18
  92. BinomialDist(len, p, I19, false) → P19
  93. BinomialDist(len, p, I20, false) → P20
  94. BinomialDist(len, p, I21, false) → P21
  95. BinomialDist(len, p, I22, false) → P22
  96. BinomialDist(len, p, I23, false) → P23
  97. BinomialDist(len, p, I24, false) → P24
  98. BinomialDist(len, p, I25, false) → P25
  99. BinomialDist(len, p, I26, false) → P26
  100. BinomialDist(len, p, I27, false) → P27
  101. BinomialDist(len, p, I28, false) → P28
  102. BinomialDist(len, p, I29, false) → P29
  103. BinomialDist(len, p, I30, false) → P30
  104. BinomialDist(len, p, I31, false) → P31
  105. BinomialDist(len, p, I32, false) → P32
  106. BinomialDist(len, p, I33, false) → P33
  107. BarChart(O2:O32, P2:P32) → d
  108. Sequence(0, k, 1, len + 1) → contador
  109. Sequence(Segment[(i - 0.5, y(B)), (i - 0.5, y(B) + höhe)], i, ((-len)) / 2, len / 2 + 1) → Liste1
  110. Textfield(len) → Textfeld1
  111. Polygon(T2, U2, U2 + (0, S2), T2 + (0, S2)) → V2, Y2, Z2, AA2, AB2
  112. Polygon(T3, U3, U3 + (0, S3), T3 + (0, S3)) → V3, Y3, Z3, AA3, AB3
  113. Polygon(T4, U4, U4 + (0, S4), T4 + (0, S4)) → V4, Y4, Z4, AA4, AB4
  114. Polygon(T5, U5, U5 + (0, S5), T5 + (0, S5)) → V5, Y5, Z5, AA5, AB5
  115. Polygon(T6, U6, U6 + (0, S6), T6 + (0, S6)) → V6, Y6, Z6, AA6, AB6
  116. Polygon(T7, U7, U7 + (0, S7), T7 + (0, S7)) → V7, Y7, Z7, AA7, AB7
  117. Polygon(T8, U8, U8 + (0, S8), T8 + (0, S8)) → V8, Y8, Z8, AA8, AB8
  118. Polygon(T9, U9, U9 + (0, S9), T9 + (0, S9)) → V9, Y9, Z9, AA9, AB9
  119. Polygon(T10, U10, U10 + (0, S10), T10 + (0, S10)) → V10, Y10, Z10, AA10, AB10
  120. Polygon(T11, U11, U11 + (0, S11), T11 + (0, S11)) → V11, Y11, Z11, AA11, AB11
  121. Polygon(T12, U12, U12 + (0, S12), T12 + (0, S12)) → V12, Y12, Z12, AA12, AB12
  122. Polygon(T13, U13, U13 + (0, S13), T13 + (0, S13)) → V13, Y13, Z13, AA13, AB13
  123. Polygon(T14, U14, U14 + (0, S14), T14 + (0, S14)) → V14, Y14, Z14, AA14, AB14
  124. Polygon(T15, U15, U15 + (0, S15), T15 + (0, S15)) → V15, Y15, Z15, AA15, AB15
  125. Polygon(T16, U16, U16 + (0, S16), T16 + (0, S16)) → V16, Y16, Z16, AA16, AB16
  126. Polygon(T17, U17, U17 + (0, S17), T17 + (0, S17)) → V17, Y17, Z17, AA17, AB17
  127. Polygon(T18, U18, U18 + (0, S18), T18 + (0, S18)) → V18, Y18, Z18, AA18, AB18
  128. Polygon(T19, U19, U19 + (0, S19), T19 + (0, S19)) → V19, Y19, Z19, AA19, AB19
  129. Polygon(T20, U20, U20 + (0, S20), T20 + (0, S20)) → V20, Y20, Z20, AA20, AB20
  130. Polygon(T21, U21, U21 + (0, S21), T21 + (0, S21)) → V21, Y21, Z21, AA21, AB21
  131. Polygon(T22, U22, U22 + (0, S22), T22 + (0, S22)) → V22, Y22, Z22, AA22, AB22
  132. Polygon(T23, U23, U23 + (0, S23), T23 + (0, S23)) → V23, Y23, Z23, AA23, AB23
  133. Polygon(T24, U24, U24 + (0, S24), T24 + (0, S24)) → V24, Y24, Z24, AA24, AB24
  134. Polygon(T25, U25, U25 + (0, S25), T25 + (0, S25)) → V25, Y25, Z25, AA25, AB25
  135. Polygon(T26, U26, U26 + (0, S26), T26 + (0, S26)) → V26, Y26, Z26, AA26, AB26
  136. Polygon(T27, U27, U27 + (0, S27), T27 + (0, S27)) → V27, Y27, Z27, AA27, AB27
  137. Polygon(T28, U28, U28 + (0, S28), T28 + (0, S28)) → V28, Y28, Z28, AA28, AB28
  138. Polygon(T29, U29, U29 + (0, S29), T29 + (0, S29)) → V29, Y29, Z29, AA29, AB29
  139. Polygon(T30, U30, U30 + (0, S30), T30 + (0, S30)) → V30, Y30, Z30, AA30, AB30
  140. Polygon(T31, U31, U31 + (0, S31), T31 + (0, S31)) → V31, Y31, Z31, AA31, AB31
  141. Polygon(T32, U32, U32 + (0, S32), T32 + (0, S32)) → V32, Y32, Z32, AA32, AB32
  142. Polygon(T33, U33, U33 + (0, S33), T33 + (0, S33)) → V33, Y33, Z33, AA33, AB33
  143. Textfield(p) → Textfeld2
  144. RemoveUndefined(V2:V33) → Balken
  145. Sum(Balken) → Versuche
  146. Polygon(T2, U2, U2 + (0, (skal * S2 / Versuche)), T2 + (0, (skal * S2 / Versuche))) → AD2, f, g, i, j
  147. Polygon(T3, U3, U3 + (0, (skal * S3 / Versuche)), T3 + (0, (skal * S3 / Versuche))) → AD3, l, n, q, r
  148. Polygon(T4, U4, U4 + (0, (skal * S4 / Versuche)), T4 + (0, (skal * S4 / Versuche))) → AD4, s, t, a_1, b_1
  149. Polygon(T5, U5, U5 + (0, (skal * S5 / Versuche)), T5 + (0, (skal * S5 / Versuche))) → AD5, c_1, d_1, e_1, f_1
  150. Polygon(T6, U6, U6 + (0, (skal * S6 / Versuche)), T6 + (0, (skal * S6 / Versuche))) → AD6, g_1, h_1, i_1, j_1
  151. Polygon(T7, U7, U7 + (0, (skal * S7 / Versuche)), T7 + (0, (skal * S7 / Versuche))) → AD7, k_1, l_1, m_1, n_1
  152. Polygon(T8, U8, U8 + (0, (skal * S8 / Versuche)), T8 + (0, (skal * S8 / Versuche))) → AD8, p_1, q_1, r_1, s_1
  153. Polygon(T9, U9, U9 + (0, (skal * S9 / Versuche)), T9 + (0, (skal * S9 / Versuche))) → AD9, t_1, a_2, b_2, c_2
  154. Polygon(T10, U10, U10 + (0, (skal * S10 / Versuche)), T10 + (0, (skal * S10 / Versuche))) → AD10, d_2, e_2, f_2, g_2
  155. Polygon(T11, U11, U11 + (0, (skal * S11 / Versuche)), T11 + (0, (skal * S11 / Versuche))) → AD11, h_2, i_2, j_2, k_2
  156. Polygon(T12, U12, U12 + (0, (skal * S12 / Versuche)), T12 + (0, (skal * S12 / Versuche))) → AD12, l_2, m_2, n_2, p_2
  157. Polygon(T13, U13, U13 + (0, (skal * S13 / Versuche)), T13 + (0, (skal * S13 / Versuche))) → AD13, q_2, r_7, s_3, t_3
  158. Polygon(T14, U14, U14 + (0, (skal * S14 / Versuche)), T14 + (0, (skal * S14 / Versuche))) → AD14, r_2, a_4, b_4, c_4
  159. Polygon(T15, U15, U15 + (0, (skal * S15 / Versuche)), T15 + (0, (skal * S15 / Versuche))) → AD15, s_2, d_5, e_5, f_5
  160. Polygon(T16, U16, U16 + (0, (skal * S16 / Versuche)), T16 + (0, (skal * S16 / Versuche))) → AD16, t_2, g_5, h_5, i_5
  161. Polygon(T17, U17, U17 + (0, (skal * S17 / Versuche)), T17 + (0, (skal * S17 / Versuche))) → AD17, a_3, j_6, k_6, l_6
  162. Polygon(T18, U18, U18 + (0, (skal * S18 / Versuche)), T18 + (0, (skal * S18 / Versuche))) → AD18, b_3, m_6, n_6, p_6
  163. Polygon(T19, U19, U19 + (0, (skal * S19 / Versuche)), T19 + (0, (skal * S19 / Versuche))) → AD19, c_3, q_6, d_4, e_4
  164. Polygon(T20, U20, U20 + (0, (skal * S20 / Versuche)), T20 + (0, (skal * S20 / Versuche))) → AD20, d_3, f_4, g_4, h_4
  165. Polygon(T21, U21, U21 + (0, (skal * S21 / Versuche)), T21 + (0, (skal * S21 / Versuche))) → AD21, e_3, i_4, j_4, k_4
  166. Polygon(T22, U22, U22 + (0, (skal * S22 / Versuche)), T22 + (0, (skal * S22 / Versuche))) → AD22, f_3, l_4, m_4, n_4
  167. Polygon(T23, U23, U23 + (0, (skal * S23 / Versuche)), T23 + (0, (skal * S23 / Versuche))) → AD23, g_3, p_4, q_4, r_4
  168. Polygon(T24, U24, U24 + (0, (skal * S24 / Versuche)), T24 + (0, (skal * S24 / Versuche))) → AD24, h_3, s_4, t_4, a_5
  169. Polygon(T25, U25, U25 + (0, (skal * S25 / Versuche)), T25 + (0, (skal * S25 / Versuche))) → AD25, i_3, b_5, c_5, j_5
  170. Polygon(T26, U26, U26 + (0, (skal * S26 / Versuche)), T26 + (0, (skal * S26 / Versuche))) → AD26, j_3, k_5, l_5, m_5
  171. Polygon(T27, U27, U27 + (0, (skal * S27 / Versuche)), T27 + (0, (skal * S27 / Versuche))) → AD27, k_3, n_5, p_5, q_5
  172. Polygon(T28, U28, U28 + (0, (skal * S28 / Versuche)), T28 + (0, (skal * S28 / Versuche))) → AD28, l_3, r_5, s_5, t_5
  173. Polygon(T29, U29, U29 + (0, (skal * S29 / Versuche)), T29 + (0, (skal * S29 / Versuche))) → AD29, m_3, a_6, b_6, c_6
  174. Polygon(T30, U30, U30 + (0, (skal * S30 / Versuche)), T30 + (0, (skal * S30 / Versuche))) → AD30, n_3, d_6, e_6, f_6
  175. Polygon(T31, U31, U31 + (0, (skal * S31 / Versuche)), T31 + (0, (skal * S31 / Versuche))) → AD31, p_3, g_6, h_6, i_6
  176. Polygon(T32, U32, U32 + (0, (skal * S32 / Versuche)), T32 + (0, (skal * S32 / Versuche))) → AD32, q_3, r_6, s_6, t_6
  177. Polygon(T33, U33, U33 + (0, (skal * S33 / Versuche)), T33 + (0, (skal * S33 / Versuche))) → AD33, r_3, a_7, b_7, c_7
  178. RemoveUndefined(AD2:AD33) → Normalisiert
  179. TableText({Liste2, Ergebnisliste, Liste3}) → Text1
  180. LaTeX(Versuche, true, true) → Text2

AI 绘图提示语参考

创建一个交互式的高尔顿板模型，展示小球下落形成的分布模式。使用多个斜线挡板，根据随机方向改变小球路径，最终在底部形成类似正态分布的积木堆。包含一个滑动条控制挡板数量，并用条形图可视化最终分布。添加文本说明核心数学概念，如二项分布和组合数学，适合高中及以上学生理解概率统计和数据可视化。
以上提示语为根据原始绘图命令整理而来，仅供参考。