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掷骰子乘以4：随机旋转与几何变换的交互演示

掷骰子乘以4：随机旋转与几何变换的交互演示
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2020-02-09 13:36
圆多边形角概率统计变换
① 本范例通过掷骰子随机生成点数，并在一个圆上以该点数对应的角度旋转多边形，直观展示“乘以4”的算术运算与几何旋转的对应关系。② 核心数学概念包括乘法、随机数、角度、旋转、多边形以及几何变换，同时涉及余弦函数在坐标计算中的应用。③ 作图要点：使用GeoGebra的Shuffle和Random命令生成随机骰子点数，通过Element从列表提取数值，利用Circle和Point构造圆周上的点，Rotate命令实现多边形旋转，Angle命令测量旋转角，Polygon和Midpoint构造图形，Textfield用于交互输入，Intersect计算交点；对象包括A至J等多个点、圆c、多边形p、q以及旋转后的副本。④ 适合小学高年级至初中学生，用于将抽象乘法与直观几何旋转结合，也可作为概率与几何变换的入门教学工具。

GeoGebra 命令及参数

  1. Shuffle(positionlist) → pl, {(21, 15), (21, 21), (15, 22), (14, 16), (3, 22), (8, 15), (2, 16), (19.234824979926557, 9.296710623986465), (9, 21), (5, 10)}
  2. Element(pl, 1) → A
  3. Element(pl, 2) → B
  4. Element(pl, 3) → C
  5. Element(pl, 4) → D
  6. Element(pl, 5) → E
  7. Element(pl, 6) → F
  8. Element(pl, 7) → G
  9. Element(pl, 8) → H
  10. Element(pl, 9) → I
  11. Element(pl, 10) → J
  12. Circle(A, sd) → c
  13. Circle(B, sd) → d
  14. Circle(C, sd) → e
  15. Circle(D, sd) → f
  16. Circle(E, sd) → g
  17. Circle(J, sd) → h
  18. Circle(I, sd) → k
  19. Circle(H, sd) → p
  20. Circle(G, sd) → q
  21. Random(90, 270) → a1
  22. Circle(F, sd) → r
  23. Point(c) → K
  24. Point(d) → L
  25. Point(e) → M
  26. Point(f) → N
  27. Point(g) → O
  28. Rotate(K, a1°, A) → K'
  29. Angle(K, A, K') → α
  30. Polygon(A, K', 4) → poly1, i, j, l, m, P, Q
  31. Random(0, 360) → a2
  32. Random(0, 360) → a3
  33. Random(0, 360) → a4
  34. Random(0, 360) → a5
  35. Random(0, 360) → a6
  36. Random(0, 360) → a7
  37. Random(0, 360) → a8
  38. Random(0, 360) → a9
  39. Random(0, 360) → a10
  40. Point(r) → R
  41. Point(q) → S
  42. Point(p) → T
  43. Point(k) → U
  44. Point(h) → V
  45. Rotate(L, a2°, B) → L'
  46. Angle(L, B, L') → β
  47. Rotate(M, a3°, C) → M'
  48. Angle(M, C, M') → γ
  49. Rotate(N, a4°, D) → N'
  50. Angle(N, D, N') → δ
  51. Rotate(O, a5°, E) → O'
  52. Angle(O, E, O') → ε
  53. Rotate(R, a6°, F) → R'
  54. Angle(R, F, R') → ζ
  55. Rotate(S, a7°, G) → S'
  56. Angle(S, G, S') → η
  57. Rotate(T, a8°, H) → T'
  58. Angle(T, H, T') → θ
  59. Rotate(U, a9°, I) → U'
  60. Angle(U, I, U') → ι
  61. Rotate(V, a10°, J) → V'
  62. Angle(V, J, V') → κ
  63. Polygon(B, L', 4) → poly2, n, s, t, a, W, Z
  64. Polygon(C, M', 4) → poly3, b, f_1, g_1, h_1, A_1, B_1
  65. Polygon(D, N', 4) → poly4, i_1, j_1, k_1, l_1, C_1, D_1
  66. Polygon(E, O', 4) → poly5, m_1, n_1, p_1, q_1, E_1, F_1
  67. Polygon(F, R', 4) → poly6, r_1, s_1, t_1, a_1, G_1, H_1
  68. Polygon(G, S', 4) → poly7, b_1, c_1, d_1, e_1, I_1, J_1
  69. Polygon(H, T', 4) → poly8, f_2, g_2, h_2, i_2, K_1, L_1
  70. Polygon(I, U', 4) → poly9, j_2, k_2, l_2, m_2, M_1, N_1
  71. Polygon(J, V', 4) → poly10, n_2, p_2, q_2, r_2, O_1, P_1
  72. Circle(J, O_1) → c_2
  73. Circle(H, K_1) → d_2
  74. Circle(G, I_1) → e_2
  75. Circle(F, G_1) → s_2
  76. Circle(E, E_1) → t_2
  77. Circle(D, C_1) → c_3
  78. Circle(C, A_1) → d_3
  79. Circle(B, W) → e_3
  80. Circle(I, M_1) → f_3
  81. Circle(A, P) → g_3
  82. Midpoint(K', Q) → Q_1
  83. Midpoint(Q_1, Q) → R_1
  84. Midpoint(K', Q_1) → S_1
  85. Midpoint(B, W) → T_1
  86. Midpoint(T_1, W) → U_1
  87. Midpoint(B, T_1) → V_1
  88. Midpoint(C, A_1) → W_1
  89. Midpoint(C, W_1) → Z_1
  90. Midpoint(W_1, A_1) → A_2
  91. Midpoint(D, C_1) → B_2
  92. Midpoint(D, B_2) → C_2
  93. Midpoint(B_2, C_1) → D_2
  94. Midpoint(E, E_1) → E_2
  95. Midpoint(E_2, E_1) → F_2
  96. Midpoint(E, E_2) → G_2
  97. Midpoint(F, G_1) → H_2
  98. Midpoint(H_2, G_1) → I_2
  99. Midpoint(F, H_2) → J_2
  100. Midpoint(G, I_1) → K_2
  101. Midpoint(G, K_2) → L_2
  102. Midpoint(I_1, K_2) → M_2
  103. Midpoint(H, K_1) → N_2
  104. Midpoint(H, N_2) → O_2
  105. Midpoint(N_2, K_1) → P_2
  106. Midpoint(J, O_1) → Q_2
  107. Midpoint(J, Q_2) → R_2
  108. Midpoint(Q_2, O_1) → S_2
  109. Midpoint(M_1, I) → T_2
  110. Midpoint(M_1, T_2) → U_2
  111. Midpoint(T_2, I) → V_2
  112. Element(dl, dsl) → dn
  113. Textfield(kiddice) → InputBox1
  114. Textfield(kiddots) → InputBox2
  115. Element(dl, dsl) → dice
  116. Intersect(j, l) → E_3
  117. Intersect(t, a) → F_3
  118. Intersect(g_1, h_1) → G_3
  119. Intersect(k_1, l_1) → H_3
  120. Intersect(p_1, q_1) → I_3
  121. Intersect(t_1, a_1) → J_3
  122. Intersect(d_1, e_1) → K_3
  123. Intersect(h_2, i_2) → L_3
  124. Intersect(l_2, m_2) → M_3
  125. Intersect(n_2, p_2) → N_3
  126. Intersect(q_2, r_2) → O_3
  127. Midpoint(A, Q_1) → P_3
  128. Midpoint(Q_1, E_3) → Q_3
  129. Midpoint(F_3, T_1) → R_3
  130. Midpoint(L', T_1) → S_3
  131. Midpoint(M', W_1) → T_3
  132. Midpoint(W_1, G_3) → U_3
  133. Midpoint(H_3, B_2) → V_3
  134. Midpoint(B_2, N') → W_3
  135. Midpoint(E_2, I_3) → Z_3
  136. Midpoint(E_2, O') → A_4
  137. Midpoint(R', H_2) → B_4
  138. Midpoint(H_2, J_3) → C_4
  139. Midpoint(K_2, S') → D_4
  140. Midpoint(K_3, K_2) → E_4
  141. Midpoint(L_3, N_2) → F_4
  142. Midpoint(N_2, T') → G_4
  143. Midpoint(U', T_2) → H_4
  144. Midpoint(T_2, M_3) → I_4
  145. Midpoint(N_3, Q_2) → J_4
  146. Midpoint(Q_2, O_3) → K_4

AI 绘图提示语参考

在画布上随机放置十个点，以其中八个点为圆心绘制大小相同的圆，另两个点分别作为旋转中心和随机角度起点。从第一个圆上取一点，绕其圆心旋转一个随机角度（90至270度之间），形成旋转后的点，并连接圆心与旋转前后两点构成角。以该圆心和旋转后的点为顶点构造一个正四边形。其余圆上各取一点，分别绕各自圆心旋转随机角度（0至360度），并测量每个旋转角。所有圆、点、旋转后的点、角及多边形共同构成一个展示随机旋转与几何变换的图形。
以上提示语为根据原始绘图命令整理而来，仅供参考。