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骰子乘法：2-6的组合与几何图形

骰子乘法：2-6的组合与几何图形
几何画板及绘图内容加载中，请稍等……
2020-02-11 15:44
三角函数概率统计参数方程几何作图
所属专题 Multiply with Dice
此范例通过GeoGebra动态演示骰子面值2、3、4、5、6的乘法组合变化，展现数字与几何图形的动态关联。核心概念涉及组合数学、概率统计与参数方程几何。作图要点包括使用Shuffle、Random、Rotate、Polygon、Intersect等命令，结合点、多边形、角度及中点构建交互式骰子乘法图。适合高中概率与几何单元，或用于课堂演示与自主探索。

GeoGebra 命令及参数

  1. Shuffle(dlist) → dl, {1, 7, 5, 4, 3, 9, 8, 6, 10, 2}
  2. Element(dl, dsl) → dice
  3. Shuffle(positionlist) → pl, {(20.841465339293297, 21.571366222300522), (2, 16), (13.792512983476586, 15.925190454706042), (14.879664839348814, 21.886990954650525), (4.53418750120986, 10.489431175344896), (8.35675370411544, 21.60643563700608), (2.184536715937622, 21.851921539944968), (20.701187680471076, 10.033528784172672), (7.865781898237659, 15.855051625294932), (19.75431348342107, 15.78491279588382)}
  4. Element(pl, 1) → A
  5. Element(pl, 2) → B
  6. Element(pl, 3) → C
  7. Element(pl, 4) → D
  8. Element(pl, 5) → E
  9. Element(pl, 6) → F
  10. Element(pl, 7) → G
  11. Element(pl, 8) → H
  12. Element(pl, 9) → I
  13. Element(pl, 10) → J
  14. Circle(A, sd) → c
  15. Circle(B, sd) → d
  16. Circle(C, sd) → e
  17. Circle(D, sd) → f
  18. Circle(E, sd) → g
  19. Circle(J, sd) → h
  20. Circle(I, sd) → k
  21. Circle(H, sd) → p
  22. Circle(G, sd) → q
  23. Random(90, 270) → a1
  24. Circle(F, sd) → r
  25. Point(c) → K
  26. Point(d) → L
  27. Point(e) → M
  28. Point(f) → N
  29. Point(g) → O
  30. Rotate(K, a1°, A) → K'
  31. Angle(K, A, K') → α
  32. Polygon(A, K', 4) → poly1, i, j, l, m, P, Q
  33. Random(0, 360) → a2
  34. Random(0, 360) → a3
  35. Random(0, 360) → a4
  36. Random(0, 360) → a5
  37. Random(0, 360) → a6
  38. Random(0, 360) → a7
  39. Random(0, 360) → a8
  40. Random(0, 360) → a9
  41. Random(0, 360) → a10
  42. Point(r) → R
  43. Point(q) → S
  44. Point(p) → T
  45. Point(k) → U
  46. Point(h) → V
  47. Rotate(L, a2°, B) → L'
  48. Angle(L, B, L') → β
  49. Rotate(M, a3°, C) → M'
  50. Angle(M, C, M') → γ
  51. Rotate(N, a4°, D) → N'
  52. Angle(N, D, N') → δ
  53. Rotate(O, a5°, E) → O'
  54. Angle(O, E, O') → ε
  55. Rotate(R, a6°, F) → R'
  56. Angle(R, F, R') → ζ
  57. Rotate(S, a7°, G) → S'
  58. Angle(S, G, S') → η
  59. Rotate(T, a8°, H) → T'
  60. Angle(T, H, T') → θ
  61. Rotate(U, a9°, I) → U'
  62. Angle(U, I, U') → ι
  63. Rotate(V, a10°, J) → V'
  64. Angle(V, J, V') → κ
  65. Polygon(B, L', 4) → poly2, n, s, t, a, W, Z
  66. Polygon(C, M', 4) → poly3, b, f_1, g_1, h_1, A_1, B_1
  67. Polygon(D, N', 4) → poly4, i_1, j_1, k_1, l_1, C_1, D_1
  68. Polygon(E, O', 4) → poly5, m_1, n_1, p_1, q_1, E_1, F_1
  69. Polygon(F, R', 4) → poly6, r_1, s_1, t_1, a_1, G_1, H_1
  70. Polygon(G, S', 4) → poly7, b_1, c_1, d_1, e_1, I_1, J_1
  71. Polygon(H, T', 4) → poly8, f_2, g_2, h_2, i_2, K_1, L_1
  72. Polygon(I, U', 4) → poly9, j_2, k_2, l_2, m_2, M_1, N_1
  73. Polygon(J, V', 4) → poly10, n_2, p_2, q_2, r_2, O_1, P_1
  74. Circle(J, O_1) → c_2
  75. Circle(H, K_1) → d_2
  76. Circle(G, I_1) → e_2
  77. Circle(F, G_1) → s_2
  78. Circle(E, E_1) → t_2
  79. Circle(D, C_1) → c_3
  80. Circle(C, A_1) → d_3
  81. Circle(B, W) → e_3
  82. Circle(I, M_1) → f_3
  83. Circle(A, P) → g_3
  84. Midpoint(K', Q) → Q_1
  85. Midpoint(Q_1, Q) → R_1
  86. Midpoint(K', Q_1) → S_1
  87. Midpoint(B, W) → T_1
  88. Midpoint(T_1, W) → U_1
  89. Midpoint(B, T_1) → V_1
  90. Midpoint(C, A_1) → W_1
  91. Midpoint(C, W_1) → Z_1
  92. Midpoint(W_1, A_1) → A_2
  93. Midpoint(D, C_1) → B_2
  94. Midpoint(D, B_2) → C_2
  95. Midpoint(B_2, C_1) → D_2
  96. Midpoint(E, E_1) → E_2
  97. Midpoint(E_2, E_1) → F_2
  98. Midpoint(E, E_2) → G_2
  99. Midpoint(F, G_1) → H_2
  100. Midpoint(H_2, G_1) → I_2
  101. Midpoint(F, H_2) → J_2
  102. Midpoint(G, I_1) → K_2
  103. Midpoint(G, K_2) → L_2
  104. Midpoint(I_1, K_2) → M_2
  105. Midpoint(H, K_1) → N_2
  106. Midpoint(H, N_2) → O_2
  107. Midpoint(N_2, K_1) → P_2
  108. Midpoint(J, O_1) → Q_2
  109. Midpoint(J, Q_2) → R_2
  110. Midpoint(Q_2, O_1) → S_2
  111. Midpoint(M_1, I) → T_2
  112. Midpoint(M_1, T_2) → U_2
  113. Midpoint(T_2, I) → V_2
  114. Element(dl, dsl) → dn
  115. Textfield(kiddice) → InputBox1
  116. Textfield(kiddots) → InputBox2
  117. Intersect(j, l) → E_3
  118. Intersect(t, a) → F_3
  119. Intersect(g_1, h_1) → G_3
  120. Intersect(k_1, l_1) → H_3
  121. Intersect(p_1, q_1) → I_3
  122. Intersect(t_1, a_1) → J_3
  123. Intersect(d_1, e_1) → K_3
  124. Intersect(h_2, i_2) → L_3
  125. Intersect(l_2, m_2) → M_3
  126. Intersect(n_2, p_2) → N_3
  127. Intersect(q_2, r_2) → O_3
  128. Midpoint(A, Q_1) → P_3
  129. Midpoint(Q_1, E_3) → Q_3
  130. Midpoint(F_3, T_1) → R_3
  131. Midpoint(L', T_1) → S_3
  132. Midpoint(M', W_1) → T_3
  133. Midpoint(W_1, G_3) → U_3
  134. Midpoint(H_3, B_2) → V_3
  135. Midpoint(B_2, N') → W_3
  136. Midpoint(E_2, I_3) → Z_3
  137. Midpoint(E_2, O') → A_4
  138. Midpoint(R', H_2) → B_4
  139. Midpoint(H_2, J_3) → C_4
  140. Midpoint(K_2, S') → D_4
  141. Midpoint(K_3, K_2) → E_4
  142. Midpoint(L_3, N_2) → F_4
  143. Midpoint(N_2, T') → G_4
  144. Midpoint(U', T_2) → H_4
  145. Midpoint(T_2, M_3) → I_4
  146. Midpoint(N_3, Q_2) → J_4
  147. Midpoint(Q_2, O_3) → K_4
  148. Midpoint(Q_3, R_1) → B_3
  149. Midpoint(S_1, P_3) → C_3
  150. Midpoint(S_3, U_1) → D_3
  151. Midpoint(V_1, R_3) → L_4
  152. Midpoint(V_3, C_2) → M_4
  153. Midpoint(D_2, W_3) → N_4
  154. Midpoint(A_2, U_3) → O_4
  155. Midpoint(T_3, Z_1) → P_4
  156. Midpoint(U_2, I_4) → Q_4
  157. Midpoint(H_4, V_2) → R_4
  158. Midpoint(C_4, J_2) → S_4
  159. Midpoint(I_2, B_4) → T_4
  160. Midpoint(P_2, G_4) → U_4
  161. Midpoint(F_4, O_2) → V_4
  162. Midpoint(E_4, M_2) → W_4
  163. Midpoint(L_2, D_4) → Z_4
  164. Midpoint(K_4, S_2) → A_5
  165. Midpoint(F_2, A_4) → B_5
  166. Midpoint(Z_3, G_2) → C_5
  167. Midpoint(R_2, J_4) → D_5

AI 绘图提示语参考

绘制两个六面骰子的组合，每个骰子的面值为2到6。首先随机生成两个骰子的位置，然后围绕每个骰子的中心点画圆。接着，随机旋转圆，并通过旋转生成新的多边形，展示两个骰子的乘积组合。
以上提示语为根据原始绘图命令整理而来，仅供参考。