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等分数的探索 by Juli Jurado i Llamas

等分数的探索 by Juli Jurado i Llamas
几何画板及绘图内容加载中，请稍等……
2016-07-19 00:38
多边形三角函数几何作图
这个范例演示了如何通过几何画板找到等分数。它涉及分数的概念，通过构造平行四边形和中位线来探索等分数的性质。使用了Polygon, Sequence, Random, IndexOf, If, Segment, Sum等命令。适合小学高年级或初中学生学习分数的等价性。

GeoGebra 命令及参数

  1. Polygon(A1, B1, 4) → Polígon1, a, b, c, d, A, B
  2. Polygon(A2, B2, 4) → Polígon2, e, f, g, h, C, D
  3. Polygon(A3, B3, 4) → Polígon3, i, j, k, l, E, F
  4. Polygon(A4, B4, 4) → Polígon4, m, n, p, q, G, H
  5. Sequence(Sample[{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, 12, false], i, 1, 10) → matriu1
  6. Random(1, 10) → fila
  7. IndexOf(1, Element[matriu1, fila]) → E1
  8. IndexOf(2, Element[matriu1, fila]) → E2
  9. IndexOf(3, Element[matriu1, fila]) → E3
  10. IndexOf(4, Element[matriu1, fila]) → E4
  11. IndexOf(5, Element[matriu1, fila]) → E5
  12. IndexOf(6, Element[matriu1, fila]) → E6
  13. IndexOf(7, Element[matriu1, fila]) → E7
  14. IndexOf(8, Element[matriu1, fila]) → E8
  15. IndexOf(9, Element[matriu1, fila]) → E9
  16. IndexOf(10, Element[matriu1, fila]) → E10
  17. IndexOf(11, Element[matriu1, fila]) → E11
  18. IndexOf(12, Element[matriu1, fila]) → E12
  19. If(Mod[E1, 3] ≟ 1, E1 + 1, If[Mod[E1, 3] ≟ 2, E1 - 1, E1 - 2]) → F1
  20. If(Mod[E2, 3] ≟ 1, E2 + 1, If[Mod[E2, 3] ≟ 2, E2 - 1, E2 - 2]) → F2
  21. If(Mod[E3, 3] ≟ 1, E3 + 1, If[Mod[E3, 3] ≟ 2, E3 - 1, E3 - 2]) → F3
  22. If(Mod[E4, 3] ≟ 1, E4 + 1, If[Mod[E4, 3] ≟ 2, E4 - 1, E4 - 2]) → F4
  23. If(Mod[E5, 3] ≟ 1, E5 + 1, If[Mod[E5, 3] ≟ 2, E5 - 1, E5 - 2]) → F5
  24. If(Mod[E6, 3] ≟ 1, E6 + 1, If[Mod[E6, 3] ≟ 2, E6 - 1, E6 - 2]) → F6
  25. If(Mod[E7, 3] ≟ 1, E7 + 1, If[Mod[E7, 3] ≟ 2, E7 - 1, E7 - 2]) → F7
  26. If(Mod[E8, 3] ≟ 1, E8 + 1, If[Mod[E8, 3] ≟ 2, E8 - 1, E8 - 2]) → F8
  27. If(Mod[E9, 3] ≟ 1, E9 + 1, If[Mod[E9, 3] ≟ 2, E9 - 1, E9 - 2]) → F9
  28. If(Mod[E10, 3] ≟ 1, E10 + 1, If[Mod[E10, 3] ≟ 2, E10 - 1, E10 - 2]) → F10
  29. If(Mod[E11, 3] ≟ 1, E11 + 1, If[Mod[E11, 3] ≟ 2, E11 - 1, E11 - 2]) → F11
  30. If(Mod[E12, 3] ≟ 1, E12 + 1, If[Mod[E12, 3] ≟ 2, E12 - 1, E12 - 2]) → F12
  31. Polygon(A5, B5, 4) → Polígon5, r, s, t, a_1, I, J
  32. Polygon(A6, B6, 4) → Polígon6, b_1, c_1, d_1, e_1, K, L
  33. Polygon(A7, B7, 4) → Polígon7, f_1, g_1, h_1, i_1, N, O
  34. Polygon(A8, B8, 4) → Polígon8, j_1, k_1, l_1, m_1, R, S
  35. Polygon(A9, B9, 4) → Polígon9, n_1, p_1, q_1, r_1, T, U
  36. Polygon(A10, B10, 4) → Polígon10, s_1, t_1, a_2, b_2, V, W
  37. Polygon(A11, B11, 4) → Polígon11, c_2, d_2, e_2, f_2, Z, A_1
  38. Polygon(A12, B12, 4) → Polígon12, g_2, h_2, i_2, j_2, B_1, C_1
  39. IndexOf(10, Element[matriu1, fila]) → o
  40. If(Mod[E1, 3] ≟ 1, E1 + 2, If[Mod[E1, 3] ≟ 2, E1 + 1, E1 - 1]) → G1
  41. If(Mod[E2, 3] ≟ 1, E2 + 2, If[Mod[E2, 3] ≟ 2, E2 + 1, E2 - 1]) → G2
  42. If(Mod[E3, 3] ≟ 1, E3 + 2, If[Mod[E3, 3] ≟ 2, E3 + 1, E3 - 1]) → G3
  43. If(Mod[E4, 3] ≟ 1, E4 + 2, If[Mod[E4, 3] ≟ 2, E4 + 1, E4 - 1]) → G4
  44. If(Mod[E5, 3] ≟ 1, E5 + 2, If[Mod[E5, 3] ≟ 2, E5 + 1, E5 - 1]) → G5
  45. If(Mod[E6, 3] ≟ 1, E6 + 2, If[Mod[E6, 3] ≟ 2, E6 + 1, E6 - 1]) → G6
  46. If(Mod[E7, 3] ≟ 1, E7 + 2, If[Mod[E7, 3] ≟ 2, E7 + 1, E7 - 1]) → G7
  47. If(Mod[E8, 3] ≟ 1, E8 + 2, If[Mod[E8, 3] ≟ 2, E8 + 1, E8 - 1]) → G8
  48. If(Mod[E9, 3] ≟ 1, E9 + 2, If[Mod[E9, 3] ≟ 2, E9 + 1, E9 - 1]) → G9
  49. If(Mod[E10, 3] ≟ 1, E10 + 2, If[Mod[E10, 3] ≟ 2, E10 + 1, E10 - 1]) → G10
  50. If(Mod[E11, 3] ≟ 1, E11 + 2, If[Mod[E11, 3] ≟ 2, E11 + 1, E11 - 1]) → G11
  51. If(Mod[E12, 3] ≟ 1, E12 + 2, If[Mod[E12, 3] ≟ 2, E12 + 1, E12 - 1]) → G12
  52. If(C1 ≟ Cell[4, E1] ∨ C1 ≟ Cell[4, F1] ∨ C1 ≟ Cell[4, G1], 1, 0) → H1
  53. If(C2 ≟ Cell[4, E2] ∨ C2 ≟ Cell[4, F2] ∨ C2 ≟ Cell[4, G2], 1, 0) → H2
  54. If(C3 ≟ Cell[4, E3] ∨ C3 ≟ Cell[4, F3] ∨ C3 ≟ Cell[4, G3], 1, 0) → H3
  55. If(C4 ≟ Cell[4, E4] ∨ C4 ≟ Cell[4, F4] ∨ C4 ≟ Cell[4, G4], 1, 0) → H4
  56. If(C5 ≟ Cell[4, E5] ∨ C5 ≟ Cell[4, F5] ∨ C5 ≟ Cell[4, G5], 1, 0) → H5
  57. If(C6 ≟ Cell[4, E6] ∨ C6 ≟ Cell[4, F6] ∨ C6 ≟ Cell[4, G6], 1, 0) → H6
  58. If(C7 ≟ Cell[4, E7] ∨ C7 ≟ Cell[4, F7] ∨ C7 ≟ Cell[4, G7], 1, 0) → H7
  59. If(C8 ≟ Cell[4, E8] ∨ C8 ≟ Cell[4, F8] ∨ C8 ≟ Cell[4, G8], 1, 0) → H8
  60. If(C9 ≟ Cell[4, E9] ∨ C9 ≟ Cell[4, F9] ∨ C9 ≟ Cell[4, G9], 1, 0) → H9
  61. If(C10 ≟ Cell[4, E10] ∨ C10 ≟ Cell[4, F10] ∨ C10 ≟ Cell[4, G10], 1, 0) → H10
  62. If(C11 ≟ Cell[4, E11] ∨ C11 ≟ Cell[4, F11] ∨ C11 ≟ Cell[4, G11], 1, 0) → H11
  63. If(C12 ≟ Cell[4, E12] ∨ C12 ≟ Cell[4, F12] ∨ C12 ≟ Cell[4, G12], 1, 0) → H12
  64. Polygon(D_1, E_1, F_1, G_1) → Polígon13, d_3, e_3, f_3, g_3
  65. Segment(G_1, D_1) → k_2
  66. Segment(D_1, E_1) → l_2
  67. Segment(E_1, F_1) → m_2
  68. Segment(F_1, G_1) → n_2
  69. Segment(H_1, M_1) → p_2
  70. Segment(L_1, Q_1) → q_2
  71. Segment(N_1, I_1) → r_2
  72. Segment(P_1, K_1) → s_2
  73. Segment(J_1, O_1) → t_2
  74. Sum(H1:H12) → H13
  75. Random(1, 10) → u
  76. Polygon(S_1, Z_1, W_1, T_1) → Polígon15, s_3, z_1, w_1, t_3
  77. If(L1 ≟ Cell[13, E1], 1, 0) → N1
  78. If(L2 ≟ Cell[13, E2], 1, 0) → N2
  79. If(L3 ≟ Cell[13, E3], 1, 0) → N3
  80. If(L4 ≟ Cell[13, E4], 1, 0) → N4
  81. If(L5 ≟ Cell[13, E5], 1, 0) → N5
  82. If(L6 ≟ Cell[13, E6], 1, 0) → N6
  83. If(L7 ≟ Cell[13, E7], 1, 0) → N7
  84. If(L8 ≟ Cell[13, E8], 1, 0) → N8
  85. If(L9 ≟ Cell[13, E9], 1, 0) → N9
  86. If(L10 ≟ Cell[13, E10], 1, 0) → N10
  87. If(L11 ≟ Cell[13, E11], 1, 0) → N11
  88. If(L12 ≟ Cell[13, E12], 1, 0) → N12
  89. Sum(N1:N12) → N13
  90. If(R1 ≟ Cell[13, E1], 1, 0) → S1
  91. If(R2 ≟ Cell[13, E2], 1, 0) → S2
  92. If(R3 ≟ Cell[13, E3], 1, 0) → S3
  93. If(R4 ≟ Cell[13, E4], 1, 0) → S4
  94. If(R5 ≟ Cell[13, E5], 1, 0) → S5
  95. If(R6 ≟ Cell[13, E6], 1, 0) → S6
  96. If(R7 ≟ Cell[13, E7], 1, 0) → S7
  97. If(R8 ≟ Cell[13, E8], 1, 0) → S8
  98. If(R9 ≟ Cell[13, E9], 1, 0) → S9
  99. If(R10 ≟ Cell[13, E10], 1, 0) → S10
  100. If(R11 ≟ Cell[13, E11], 1, 0) → S11
  101. If(R12 ≟ Cell[13, E12], 1, 0) → S12
  102. Sum(S1:S12) → S13

AI 绘图提示语参考

绘制四个平行四边形，每个由四个点组成。然后随机选择12个数字，根据这些数字生成一系列新的数字，通过加减1或2来调整。最后，用这些新的数字作为点的坐标，绘制另外四个平行四边形。
以上提示语为根据原始绘图命令整理而来，仅供参考。