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整数乘法游戏

整数乘法游戏
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2015-05-26 01:17
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所属专题 Introduction to Integers and Integer Arithmetics Introduction to Integers and Integer Arithmetics
①本范例是一个交互式小程序，用于演示整数乘法的计算过程；②涉及的核心数学概念包括整数运算、几何变换和随机数生成；③作图要点使用了RandomElement（随机元素）、Polygon（多边形）、Point（点）、Rotate（旋转）、Midpoint（中点）、Segment（线段）等GeoGebra命令；④适合小学或初中阶段的学生进行数学练习和游戏化学习。

GeoGebra 命令及参数

  1. RandomElement({-3, -2, -1, 1, 2, 3}) → r1
  2. Polygon(A, B, C, D) → poly1, a, b, c, d
  3. Point(Circle[E, a]) → F
  4. Rotate(F + (b, 0), Angle[C - B] + Angle[F - E] - Angle[B - A], F) → G
  5. Rotate(G + (c, 0), Angle[D - C] + Angle[G - F] - Angle[C - B], G) → H
  6. Polygon(E, F, G, H) → poly2, e, f, g, h
  7. Point(Circle[I, e]) → J
  8. Rotate(J + (f, 0), Angle[G - F] + Angle[J - I] - Angle[F - E], J) → K
  9. Rotate(K + (g, 0), Angle[H - G] + Angle[K - J] - Angle[G - F], K) → L
  10. Polygon(I, J, K, L) → poly3, i, j, k, l
  11. Point(Circle[M, i]) → N
  12. Rotate(N + (j, 0), Angle[K - J] + Angle[N - M] - Angle[J - I], N) → O
  13. Rotate(O + (k, 0), Angle[L - K] + Angle[O - N] - Angle[K - J], O) → P
  14. Polygon(M, N, O, P) → poly4, m, n, o, p
  15. Point(Circle[Q, a]) → R
  16. Rotate(R + (b, 0), Angle[C - B] + Angle[R - Q] - Angle[B - A], R) → S
  17. Rotate(S + (c, 0), Angle[D - C] + Angle[S - R] - Angle[C - B], S) → T
  18. Polygon(Q, R, S, T) → poly5, q, r, s, t
  19. Point(Circle[U, e]) → V
  20. Rotate(V + (f, 0), Angle[G - F] + Angle[V - U] - Angle[F - E], V) → W
  21. Rotate(W + (g, 0), Angle[H - G] + Angle[W - V] - Angle[G - F], W) → Z
  22. Polygon(U, V, W, Z) → poly6, u, v, w, z_1
  23. Point(Circle[A_1, i]) → B_1
  24. Rotate(B_1 + (j, 0), Angle[K - J] + Angle[B_1 - A_1] - Angle[J - I], B_1) → C_1
  25. Rotate(C_1 + (k, 0), Angle[L - K] + Angle[C_1 - B_1] - Angle[K - J], C_1) → D_1
  26. Polygon(A_1, B_1, C_1, D_1) → poly7, a_1, b_1, c_1, d_1
  27. Point(Circle[E_1, m]) → F_1
  28. Rotate(F_1 + (n, 0), Angle[O - N] + Angle[F_1 - E_1] - Angle[N - M], F_1) → G_1
  29. Rotate(G_1 + (o, 0), Angle[P - O] + Angle[G_1 - F_1] - Angle[O - N], G_1) → H_1
  30. Polygon(E_1, F_1, G_1, H_1) → poly8, e_1, f_1, g_1, h_1
  31. Point(Circle[I_1, q]) → J_1
  32. Rotate(J_1 + (r, 0), Angle[S - R] + Angle[J_1 - I_1] - Angle[R - Q], J_1) → K_1
  33. Rotate(K_1 + (s, 0), Angle[T - S] + Angle[K_1 - J_1] - Angle[S - R], K_1) → L_1
  34. Polygon(I_1, J_1, K_1, L_1) → poly9, i_1, j_1, k_1, l_1
  35. Point(Circle[N_1, a]) → O_1
  36. Rotate(O_1 + (b, 0), Angle[C - B] + Angle[O_1 - N_1] - Angle[B - A], O_1) → P_1
  37. Rotate(P_1 + (c, 0), Angle[D - C] + Angle[P_1 - O_1] - Angle[C - B], P_1) → Q_1
  38. Polygon(N_1, O_1, P_1, Q_1) → poly10, n_1, o_1, p_1, q_1
  39. Point(Circle[R_1, e]) → S_1
  40. Rotate(S_1 + (f, 0), Angle[G - F] + Angle[S_1 - R_1] - Angle[F - E], S_1) → T_1
  41. Rotate(T_1 + (g, 0), Angle[H - G] + Angle[T_1 - S_1] - Angle[G - F], T_1) → U_1
  42. Polygon(R_1, S_1, T_1, U_1) → poly11, r_1, s_1, t_1, u_1
  43. Point(Circle[V_1, i]) → W_1
  44. Rotate(W_1 + (j, 0), Angle[K - J] + Angle[W_1 - V_1] - Angle[J - I], W_1) → Z_1
  45. Rotate(Z_1 + (k, 0), Angle[L - K] + Angle[Z_1 - W_1] - Angle[K - J], Z_1) → A_2
  46. Polygon(V_1, W_1, Z_1, A_2) → poly12, v_1, w_1, z_2, a_2
  47. Point(Circle[B_2, m]) → C_2
  48. Rotate(C_2 + (n, 0), Angle[O - N] + Angle[C_2 - B_2] - Angle[N - M], C_2) → D_2
  49. Rotate(D_2 + (o, 0), Angle[P - O] + Angle[D_2 - C_2] - Angle[O - N], D_2) → E_2
  50. Polygon(B_2, C_2, D_2, E_2) → poly13, b_2, c_2, d_2, e_2
  51. Point(Circle[F_2, q]) → G_2
  52. Rotate(G_2 + (r, 0), Angle[S - R] + Angle[G_2 - F_2] - Angle[R - Q], G_2) → H_2
  53. Rotate(H_2 + (s, 0), Angle[T - S] + Angle[H_2 - G_2] - Angle[S - R], H_2) → I_2
  54. Polygon(F_2, G_2, H_2, I_2) → poly14, f_2, g_2, h_2, i_2
  55. Point(Circle[J_2, u]) → K_2
  56. Rotate(K_2 + (v, 0), Angle[W - V] + Angle[K_2 - J_2] - Angle[V - U], K_2) → L_2
  57. Rotate(L_2 + (w, 0), Angle[Z - W] + Angle[L_2 - K_2] - Angle[W - V], L_2) → M_2
  58. Polygon(J_2, K_2, L_2, M_2) → poly15, j_2, k_2, l_2, m_2
  59. Point(Circle[N_2, a_1]) → O_2
  60. Rotate(O_2 + (b_1, 0), Angle[C_1 - B_1] + Angle[O_2 - N_2] - Angle[B_1 - A_1], O_2) → P_2
  61. Rotate(P_2 + (c_1, 0), Angle[D_1 - C_1] + Angle[P_2 - O_2] - Angle[C_1 - B_1], P_2) → Q_2
  62. Polygon(N_2, O_2, P_2, Q_2) → poly16, n_2, o_2, p_2, q_2
  63. Point(Circle[R_2, e_1]) → S_2
  64. Rotate(S_2 + (f_1, 0), Angle[G_1 - F_1] + Angle[S_2 - R_2] - Angle[F_1 - E_1], S_2) → T_2
  65. Rotate(T_2 + (g_1, 0), Angle[H_1 - G_1] + Angle[T_2 - S_2] - Angle[G_1 - F_1], T_2) → U_2
  66. Polygon(R_2, S_2, T_2, U_2) → poly17, r_2, s_2, t_2, u_2
  67. Point(Circle[V_2, i_1]) → W_2
  68. Rotate(W_2 + (j_1, 0), Angle[K_1 - J_1] + Angle[W_2 - V_2] - Angle[J_1 - I_1], W_2) → Z_2
  69. Rotate(Z_2 + (k_1, 0), Angle[L_1 - K_1] + Angle[Z_2 - W_2] - Angle[K_1 - J_1], Z_2) → A_3
  70. Polygon(V_2, W_2, Z_2, A_3) → poly18, v_2, w_2, z_3, a_3
  71. Point(Circle[M_1, b_2]) → B_3
  72. Rotate(B_3 + (c_2, 0), Angle[D_2 - C_2] + Angle[B_3 - M_1] - Angle[C_2 - B_2], B_3) → C_3
  73. Rotate(C_3 + (d_2, 0), Angle[E_2 - D_2] + Angle[C_3 - B_3] - Angle[D_2 - C_2], C_3) → D_3
  74. Polygon(M_1, B_3, C_3, D_3) → poly19, m_1, b_3, c_3, d_3
  75. Point(Circle[E_3, v_1]) → F_3
  76. Rotate(F_3 + (w_1, 0), Angle[Z_1 - W_1] + Angle[F_3 - E_3] - Angle[W_1 - V_1], F_3) → G_3
  77. Rotate(G_3 + (z_2, 0), Angle[A_2 - Z_1] + Angle[G_3 - F_3] - Angle[Z_1 - W_1], G_3) → H_3
  78. Polygon(E_3, F_3, G_3, H_3) → poly20, e_3, f_3, g_3, h_3
  79. Point(Circle[I_3, f_2]) → J_3
  80. Rotate(J_3 + (g_2, 0), Angle[H_2 - G_2] + Angle[J_3 - I_3] - Angle[G_2 - F_2], J_3) → K_3
  81. Rotate(K_3 + (h_2, 0), Angle[I_2 - H_2] + Angle[K_3 - J_3] - Angle[H_2 - G_2], K_3) → L_3
  82. Polygon(I_3, J_3, K_3, L_3) → poly21, i_3, j_3, k_3, l_3
  83. Point(Circle[M_3, j_2]) → N_3
  84. Rotate(N_3 + (k_2, 0), Angle[L_2 - K_2] + Angle[N_3 - M_3] - Angle[K_2 - J_2], N_3) → O_3
  85. Rotate(O_3 + (l_2, 0), Angle[M_2 - L_2] + Angle[O_3 - N_3] - Angle[L_2 - K_2], O_3) → P_3
  86. Polygon(M_3, N_3, O_3, P_3) → poly22, m_3, n_3, o_3, p_3
  87. Point(Circle[Q_3, n_2]) → R_3
  88. Rotate(R_3 + (o_2, 0), Angle[P_2 - O_2] + Angle[R_3 - Q_3] - Angle[O_2 - N_2], R_3) → S_3
  89. Rotate(S_3 + (p_2, 0), Angle[Q_2 - P_2] + Angle[S_3 - R_3] - Angle[P_2 - O_2], S_3) → T_3
  90. Polygon(Q_3, R_3, S_3, T_3) → poly23, q_3, r_3, s_3, t_3
  91. Point(Circle[U_3, r_2]) → V_3
  92. Rotate(V_3 + (s_2, 0), Angle[T_2 - S_2] + Angle[V_3 - U_3] - Angle[S_2 - R_2], V_3) → W_3
  93. Rotate(W_3 + (t_2, 0), Angle[U_2 - T_2] + Angle[W_3 - V_3] - Angle[T_2 - S_2], W_3) → Z_3
  94. Polygon(U_3, V_3, W_3, Z_3) → poly24, u_3, v_3, w_3, z_4
  95. Point(Circle[A_4, a]) → B_4
  96. Rotate(B_4 + (b, 0), Angle[C - B] + Angle[B_4 - A_4] - Angle[B - A], B_4) → C_4
  97. Rotate(C_4 + (c, 0), Angle[D - C] + Angle[C_4 - B_4] - Angle[C - B], C_4) → D_4
  98. Polygon(A_4, B_4, C_4, D_4) → poly25, a_4, b_4, c_4, d_4
  99. Midpoint(G_4, F_4) → Center
  100. Segment(H_4, I_4) → f_4
  101. Segment(J_4, K_4) → g_4

AI 绘图提示语参考

创建一个展示整数乘法的交互式几何游戏。使用随机生成的正负整数作为初始值，通过几何变换构建多个多边形。每个多边形依次围绕中心点旋转特定角度并平移，形成一系列形状相似但位置不同的图形。最终展示多个多边形组合的动态效果，用于教学演示。
以上提示语为根据原始绘图命令整理而来，仅供参考。