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分数加法演示 by Daniel Mentrard

分数加法演示 by Daniel Mentrard
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2020-02-28 15:42
多边形向量几何作图
①本范例演示了分数加法的几何直观表达，通过图形变换展示分数相加的过程；②涉及核心数学概念包括分数运算、几何变换、向量与多边形构造；③作图要点运用了Mod、Segment、Translate、Rotate、Sequence、Polygon、Vector等GeoGebra命令与对象，实现图形的精确构造与动态演示；④适合初中及以上数学教学，用于辅助理解分数加法与几何变换的关联，提升空间想象能力。

GeoGebra 命令及参数

  1. Mod((q * m), p) → qq
  2. Segment(A, B) → a
  3. Segment(A, D) → b
  4. Segment(D, C) → c
  5. Segment(C, B) → d
  6. Translate(E, Vector[A, B]) → F
  7. Rotate(F, 90°, E) → H
  8. Rotate(E, 90°, H) → G
  9. Segment(E, F) → e
  10. Segment(F, G) → f
  11. Segment(G, H) → g
  12. Segment(H, E) → h
  13. Sequence(Segment[A + ((i * w / p), 0), A + ((i * w / p), w)], i, 1, p - 1) → list1
  14. Sequence(Segment[E + ((i * w / p), 0), E + ((i * w / p), w)], i, 1, p - 1) → list2
  15. Sequence(Segment[A + (0, (i * w / m)), A + (w, (i * w / m))], i, 1, m - 1) → list3
  16. Sequence(Segment[E + (0, (i * w / m)), E + (w, (i * w / m))], i, 1, m - 1) → list4
  17. Polygon(E, E + (w, 0), E + (w, (n / m * w)), E + (0, (n / m * w))) → poly1, e_1, i, j, k
  18. Polygon(A, A + ((q / p * w), 0), A + ((q / p * w), w), A + (0, w)) → poly2, a_1, l, r, s_1
  19. Polygon(I, I + (w, 0), I + (w, (n / m * w)), I + (0, (n / m * w))) → poly3, i_1, s, t, b_1
  20. Sequence(Segment[I + (0, (i * w / m)), I + (w, (i * w / m))], i, 1, m - 1) → liste1
  21. Sequence(Segment[M + ((i * w / p), 0), M + ((i * w / p), w)], i, 1, p - 1) → liste2
  22. Polygon(I, J, K, L) → poly4, i_2, j_1, k_1, l_1
  23. Polygon(M, M + ((q / p * w), 0), M + ((q / p * w), w), M + (0, w)) → poly5, m_1, c_1, d_1, f_1
  24. Polygon(M, N, O, P) → poly6, m_2, n_1, o_1, p_1
  25. Vector(E, Q) → u
  26. Translate(G, u) → G'
  27. Translate(H, u) → H'
  28. Segment(G', H') → g'
  29. Translate(list2, u) → list2'
  30. Translate(F, u) → F'
  31. Translate(G, u) → G'_1
  32. Segment(F', G'_1) → f'
  33. Translate(H, u) → H'_1
  34. Translate(E, u) → E'
  35. Segment(H'_1, E') → h'
  36. Translate(E, u) → E'_1
  37. Translate(F, u) → F'_1
  38. Segment(E'_1, F'_1) → e'
  39. Translate(poly1, u) → poly1'
  40. Translate(list4, u) → list4'
  41. Vector(A, T) → v
  42. Translate(C, v) → C'
  43. Translate(B, v) → B'
  44. Segment(C', B') → d'
  45. Translate(list3, v) → list3'
  46. Translate(A, v) → A'
  47. Translate(B, v) → B'_1
  48. Segment(A', B'_1) → a'
  49. Translate(list1, v) → list1'
  50. Translate(D, v) → D'
  51. Translate(C, v) → C'_1
  52. Segment(D', C'_1) → c'
  53. Translate(A, v) → A'_1
  54. Translate(D, v) → D'_1
  55. Segment(A'_1, D'_1) → b'
  56. Polygon(V, W, B', T) → poly8, v_1, w_1, b'_1, t_1
  57. Polygon(Z, B_1, A_1, V) → poly9, z, b_2, a_2, v_2
  58. Vector(T, R) → u_1
  59. Translate(V, u_1) → V'
  60. Translate(W, u_1) → W'
  61. Translate(B', u_1) → B''
  62. Translate(T, u_1) → T'
  63. Polygon(V', W', B'', T') → poly8', v', w', b'', t'
  64. Translate(Z, u_1) → Z'
  65. Translate(B_1, u_1) → S
  66. Translate(A_1, u_1) → C_1
  67. Translate(V, u_1) → V'_1
  68. Polygon(Z', S, C_1, V'_1) → poly9', z', s_2, c_2, v'_1
  69. CircumcircleArc(D_1, E_1, F_1) → g_1
  70. Point(g_1) → G_1
  71. Vector(G_1, F_1) → z_1
  72. Line(H_1, I_1) → h_1
  73. Line(J_1, K_1) → q_1
  74. Segment(W', B'') → r_1
  75. Segment(V', W') → d_2
  76. Segment(W', B'') → f_2
  77. Segment(V'_1, T') → g_2
  78. Segment(V'_1, Z') → h_2
  79. Segment(S, C_1) → j_2
  80. Vector(L_1, M_1) → u_2
  81. Vector(N_1, O_1) → w_2
  82. Sequence(Segment[V'_1 + ((i * w / p), 0), Z' + ((i * w / p), 0)], i, 1, p) → liste42
  83. Sequence(Segment[T' + ((i * w / p), 0), V' + ((i * w / p), 0)], i, 1, p) → liste41
  84. Translate(P_1, u_1) → Q_1
  85. Segment(Z', Q_1) → e_2
  86. Segment(W', G') → k_2
  87. Sequence(Segment[T' + (0, (i * w / m)), T' + (w, (i * w / m))], i, 1, pp) → liste40
  88. Line(R_1, S_1) → l_2