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对数性质动态演示 by Tim Brzezinski (3)

对数性质动态演示 by Tim Brzezinski (3)
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2017-04-28 01:20
函数几何作图
所属专题 Exponential & Logarithmic Functions Exponential & Logarithmic Functions
①本范例演示对数函数的动态性质与可修改性；②涉及核心数学概念包括对数函数、几何变换、向量运算；③构造中运用了Textfield, Intersect, Dilate, Segment, Vector, Translate, Rotate, Distance等GeoGebra命令与对象；④适合高中及以上数学教学与探索性学习。

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. Translate(A'_2, v) → K
  25. Rotate(K, If[3 < d ≤ 4, ((-(d - 3)) * π / 2), ((-π)) / 2], F) → K'
  26. Intersect(f, p, 1) → N
  27. Rotate(F, If[5 < d ≤ 6, ((d - 5) * π / 2), π / 2], F) → F'_1
  28. Rotate(F', If[5 < d ≤ 6, ((d - 5) * π / 2), π / 2], F) → F''
  29. Dilate(F, If[6 < d ≤ 7, 7 - d, 0], M) → F'_2
  30. Vector(F, F'_2) → w
  31. Translate(F'_1, w) → P
  32. Translate(F'', w) → F'''
  33. Distance(A, C) → distanceAC
  34. Vector(A, A'_2) → i
  35. Dilate(Q, If[3 < d ≤ 4, 4 - d, 0], V) → Q'
  36. Vector(Q, Q') → v_1
  37. Distance(Q, V) → distanceQV
  38. Vector(A, C') → b_1
  39. Translate(i, b_1) → i'
  40. Translate(C, b_1) → C'_1
  41. Vector(K, C'_1) → e
  42. Distance(K, C'_1) → distanceKC'1
  43. Dilate(Q, If[4 < d ≤ 5, 5 - d, 0], C'_1) → Q'_1
  44. Vector(Q, Q'_1) → q
  45. Translate(V, q) → V'
  46. Vector(Q'_1, V') → u_1
  47. Distance(Q'_1, V') → distanceQ'1V'
  48. Dilate(W, If[6 < d ≤ 7, 7 - d, 0], L) → W'
  49. Vector(W, W') → w_1
  50. Distance(W, L) → distanceWL