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对数运算性质动态演示

对数运算性质动态演示
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2017-04-28 20:44
函数几何作图
所属专题 Exponential & Logarithmic Functions
①本范例动态演示对数运算的幂性质，通过可视化方式展现对数函数与多边形、向量等几何元素的交互；②核心数学概念包括对数函数、幂运算、几何变换、向量运算；③构造要点运用了Textfield, Intersect, Dilate, Segment, Vector, Translate, Rotate, Distance, Midpoint, Line, Circle等GeoGebra命令与对象，实现图形的动态生成与变换；④适合高中及以上数学教学，用于理解对数性质及几何应用。

GeoGebra 命令及参数

  1. Textfield(a) → InputBox1
  2. Textfield(f_1) → InputBox2
  3. Textfield(f) → InputBox3
  4. Intersect(f, h, 1) → E
  5. Dilate(F, If[0 < d ≤ 1, 1 - d, 0], A) → F'
  6. Dilate(A, If[1 < d ≤ 2, 2 - d, 0], B) → A'
  7. Segment(A, A') → j
  8. Dilate(B, If[2 < d ≤ 3, 3 - d, 0], G) → B'
  9. Vector(B, B') → u
  10. Translate(A, u) → A'_1
  11. Translate(A', u) → A''
  12. Segment(A'_1, A'') → j'
  13. Rotate(A'_1, If[3 < d ≤ 4, ((-(d - 3)) * π / 2), ((-π)) / 2], F) → H
  14. Rotate(A'', If[3 < d ≤ 4, ((-(d - 3)) * π / 2), ((-π)) / 2], F) → A'''
  15. Segment(H, A''') → j''
  16. Rotate(A'_1, If[3 < d ≤ 4, ((d - 3) * π / 2), π / 2], F) → I
  17. Rotate(A'', If[3 < d ≤ 4, ((d - 3) * π / 2), π / 2], F) → A'''_1
  18. Dilate(D, If[4 < d ≤ 5, 5 - d, 0], E) → D'
  19. Segment(D, D') → l
  20. Dilate(A, If[1 < d ≤ 2, 2 - d, 0], C) → A'_2
  21. Segment(A, A'_2) → m
  22. Dilate(A, If[2 < d ≤ 3, 3 - d, 0], R) → C'
  23. Vector(C, C') → v
  24. Intersect(f, p, 1) → N
  25. Rotate(F, If[5 < d ≤ 6, ((d - 5) * π / 2), π / 2], F) → F'_1
  26. Rotate(F', If[5 < d ≤ 6, ((d - 5) * π / 2), π / 2], F) → F''
  27. Dilate(F, If[6 < d ≤ 7, 7 - d, 0], M) → F'_2
  28. Vector(F, F'_2) → w
  29. Translate(F'_1, w) → P
  30. Translate(F'', w) → F'''
  31. Distance(A, C) → distanceAC
  32. Vector(A, A'_2) → i
  33. Vector(A, C') → b_1
  34. Midpoint(Z, A_1) → Q
  35. Line(B_1, C_1) → e
  36. Segment(B_1, C_1) → g_1
  37. Circle(B_1, g_1 / 3) → c_1
  38. Intersect(c_1, e, 2) → T
  39. Circle(T, g_1 / 3) → d_1
  40. Intersect(d_1, e, 2) → U
  41. Dilate(Z, If[2 < d ≤ 3, 3 - d, 0], Q) → Z'
  42. Segment(Z, Z') → q
  43. Dilate(Q, If[3 < d ≤ 4, 4 - d, 0], A_1) → Q'
  44. Segment(Q, Q') → h_1
  45. Dilate(B_1, If[4 < d ≤ 5, 5 - d, 0], T) → D_1
  46. Segment(B_1, D_1) → i_1
  47. Dilate(T, If[5 < d ≤ 6, 6 - d, 0], U) → T'
  48. Segment(T, T') → j_1
  49. Dilate(U, If[6 < d ≤ 7, 7 - d, 0], C_1) → U'
  50. Segment(U, U') → k_1
  51. Segment(A, A'_2) → l_1
  52. Distance(Z, A_1) → distanceZA1
  53. Distance(B_1, C_1) → distanceB1C1
  54. Dilate(A, If[7 < d ≤ 8, 8 - d, 0], Z) → A'_3
  55. Vector(A, A'_3) → u_1
  56. Dilate(A, If[7 < d ≤ 8, 8 - d, 0], B_1) → A'_4
  57. Vector(A, A'_4) → v_1
  58. Translate(A, u_1) → A'_5
  59. Translate(A'_2, u_1) → L
  60. Segment(A'_5, L) → m_1
  61. Translate(A, v_1) → A'_6
  62. Translate(A'_2, v_1) → W
  63. Segment(A'_6, W) → n_1
  64. Rotate(A'_5, If[8 < d ≤ 9, ((d - 8) * π), π], Q) → E_1
  65. Rotate(L, If[8 < d ≤ 9, ((d - 8) * π), π], Q) → L'
  66. Segment(E_1, L') → p_1
  67. Rotate(A'_6, If[8 < d ≤ 9, ((d - 8) * π), π], T) → F_1
  68. Rotate(W, If[8 < d ≤ 9, ((d - 8) * π), π], T) → W'
  69. Segment(F_1, W') → q_1
  70. Rotate(F_1, If[9 < d ≤ 10, ((d - 9) * π), π], U) → G_1
  71. Rotate(W', If[9 < d ≤ 10, ((d - 9) * π), π], U) → W''
  72. Segment(G_1, W'') → r_1