有理数加减法几何模型 by Matthew Cox

有理数加减法几何模型 by Matthew Cox
几何画板及绘图内容加载中,请稍等……
2014-12-02 05:11
这个范例演示了有理数的加减法,通过几何图形直观展示运算过程。核心数学概念包括有理数及其加减法。使用了Line, Point, Circle, Vector, Translate, Segment, Midpoint等GeoGebra命令。适合初中数学教学,帮助学生理解有理数的加减法几何意义。

GeoGebra 命令及参数

  1. Line(A, B) → a
  2. Point(a) → C
  3. Circle(C, 4) → k
  4. OrthogonalLine(C, a) → d
  5. Intersect(k, d, 1) → J_1
  6. Circle(C, 2) → p
  7. Intersect(p, d) → I_1, L_5
  8. Vector(L_5, P_2) → u_1
  9. Circle(M_1, 1) → q
  10. Circle(L_5, 1) → g
  11. Intersect(g, d, 1) → N_1
  12. OrthogonalLine(N_1, d) → i
  13. Intersect(q, i) → O_1, P_1
  14. Intersect(p, d, 1) → M_2
  15. Vector(I_1, L_1) → v
  16. Intersect(k, d, 2) → R_1
  17. Circle(R_1, N_1) → r
  18. Intersect(r, d, 2) → S_1
  19. Circle(M_3, 1) → q_1
  20. Intersect(q_1, i_1, 1) → N_2
  21. Translate(N_2, v) → Q_2
  22. Point(a) → D
  23. Point(a) → E
  24. Point(a) → F
  25. Point(a) → G
  26. Point(a) → H
  27. Point(a) → I
  28. Point(a) → J
  29. Point(a) → K
  30. Point(a) → L
  31. Point(a) → M
  32. Point(a) → N
  33. Point(a) → O
  34. Point(a) → P
  35. Point(a) → Q
  36. Point(a) → R
  37. Point(a) → S
  38. Point(a) → T
  39. Point(a) → U
  40. Point(a) → V
  41. Point(a) → W
  42. Point(a) → Y
  43. Point(a) → Z
  44. Point(a) → A_1
  45. Point(a) → B_1
  46. Point(a) → C_1
  47. Point(a) → D_1
  48. Point(a) → E_1
  49. Point(a) → F_1
  50. Point(a) → G_1
  51. Point(a) → H_1
  52. OrthogonalLine(I_1, d) → e
  53. OrthogonalLine(L_5, d) → h
  54. OrthogonalLine(J_1, d) → f
  55. Vector(J_1, K_1) → u
  56. Vector(L_5, M_1) → w
  57. Translate(O_1, u_1) → Q_1
  58. Vector(O_1, Q_1) → z
  59. OrthogonalLine(S_1, d) → j
  60. Vector(S_1, T_1) → l
  61. Segment(J_1, S_1) → m
  62. Segment(M_1, O_1) → t
  63. OrthogonalLine(K_1, a) → n
  64. Intersect(n, a) → U_1
  65. OrthogonalLine(L_1, a) → s
  66. OrthogonalLine(T_1, a) → a_1
  67. Intersect(s, a) → W_1
  68. Intersect(a_1, a) → Y_1
  69. Segment(T_1, Y_1) → c_1
  70. Segment(L_1, W_1) → d_1
  71. Segment(I_1, L_1) → b_2
  72. Segment(J_1, K_1) → e_1
  73. Segment(L_5, M_1) → f_1
  74. Segment(T_1, S_1) → h_1
  75. Midpoint(J_1, K_1) → Z_1
  76. Midpoint(I_1, L_1) → A_2
  77. Midpoint(L_5, M_1) → B_2
  78. Midpoint(Q_1, O_1) → C_2
  79. Point(a) → V_1
  80. Point(a) → D_2
  81. Point(a) → E_2
  82. Point(a) → F_2
  83. Point(a) → G_2
  84. Point(a) → H_2
  85. Point(a) → I_2
  86. Point(a) → J_2
  87. Point(a) → K_2
  88. Point(a) → L_2
  89. Circle(M_2, 1) → g_1
  90. Vector(M_2, M_3) → w_1
  91. Vector(N_2, Q_2) → z_1
  92. Midpoint(Q_2, N_2) → C_3
  93. Midpoint(M_2, M_3) → O_2
  94. Segment(N_2, M_4) → j_1
  95. OrthogonalLine(P_2, a) → s_1
  96. OrthogonalLine(R_2, a) → k_1
  97. OrthogonalLine(P_2, a) → l_1
  98. Mirror(Q_1, O_1) → T_2
  99. Vector(O_1, T_2) → v_1
  100. Midpoint(T_2, O_1) → U_2
  101. OrthogonalLine(T_2, a) → m_1
  102. Intersect(m_1, a) → S_2

AI 绘图提示语参考

在一条水平直线上,先确定两个固定点并画一条直线,再在直线上取一个点作为圆心,分别以半径4和2画两个同心圆。过圆心作直线的垂线,与两个圆相交,得到多个交点。利用这些交点构造向量,并通过平移和画小圆的方式,在直线上下方生成一系列等距的点,表示整数加法和减法的几何过程。最后在直线上均匀放置多个点,作为数轴上的整数刻度,整体呈现一个结合圆、垂线、向量和平移的几何数轴模型。
以上提示语为根据原始绘图命令整理而来,仅供参考。